Glossary of general topology

This glossary provides definitions of the basic terms used in general topology . Links in italics are in italics .

# A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A

Discrete Topology: Topology in space $X$ ${\ displaystyle X}$ in which only two sets are open: the space itself $X$ ${\ displaystyle X}$ and empty set.

B

Topology base: A set of open sets, such that any open set is a union of sets from the base.

To

Topological Space Weight: The minimum capacity of all the bases of space.
Real full space: A space homeomorphic to a closed subspace of some degree of a real line.
Interior: The set of all interior points of the set . The largest open subset of a given set by inclusion.
The interior point of the set: A point that is included in this set along with some of its surroundings .
Inscribed coverage: Coating $A$ ${\ displaystyle A}$ inscribed in the coating $B$ ${\ displaystyle B}$ if each set of $A$ ${\ displaystyle A}$ contained in any set of $B$ ${\ displaystyle B}$
Completely incoherent space: A space in which no subset containing more than one point is connected .
Everywhere dense multitude: A set whose closure coincides with the whole space.
Punctured neighborhood: The neighborhood of this point from which this point itself was deleted.

R

Homeomorphism: Bijection $f$ ${\ displaystyle f}$ such that $f$ ${\ displaystyle f}$ and $f^{-1}$ ${\ displaystyle f ^ {- 1}}$ continuous .
Homeomorphic spaces: The spaces between which there is a homeomorphism .
Homotopy: For continuous display $f\colon X\to Y$ ${\ displaystyle f \ colon X \ to Y}$ - continuous display $F\colon [0,\;1]\times X\to Y$ ${\ displaystyle F \ colon [0, \; 1] \ times X \ to Y}$ such that $F(0,\;x)=f(x)$ ${\ displaystyle F (0, \; x) = f (x)}$ for anyone $x\in X$ ${\ displaystyle x \ in X}$ . Often used designation $f_{t}(x)=F(t,\;x)$ ${\ displaystyle f_ {t} (x) = F (t, \; x)}$ , in particular $f_{0}=f$ ${\ displaystyle f_ {0} = f}$ .
Homotopic mappings: Mappings $f,\;g\colon X\to Y$ ${\ displaystyle f, \; g \ colon X \ to Y}$ are called homotopic or $g\sim f$ ${\ displaystyle g \ sim f}$ if there is homotopy $f_{t}$ ${\ displaystyle f_ {t}}$ such that $f_{0}=f$ ${\ displaystyle f_ {0} = f}$ and $f_{1}=g$ ${\ displaystyle f_ {1} = g}$ .
Homotopy equivalence of topological spaces: Topological spaces $X$ ${\ displaystyle X}$ and $Y$ ${\ displaystyle Y}$ homotopy equivalent if there is a pair of continuous mappings $f\colon X\to Y$ ${\ displaystyle f \ colon X \ to Y}$ and $g\colon Y\to X$ ${\ displaystyle g \ colon Y \ to X}$ such that $f\circ g\sim \mathrm {id} _{Y}$ ${\ displaystyle f \ circ g \ sim \ mathrm {id} _ {Y}}$ and $g\circ f\sim \mathrm {id} _{X}$ ${\ displaystyle g \ circ f \ sim \ mathrm {id} _ {X}}$ , here $\sim$ ${\ displaystyle \ sim}$ denotes the homotopy equivalence of mappings , that is, equivalence up to homotopy . They also say that $X$ ${\ displaystyle X}$ and $Y$ ${\ displaystyle Y}$ have one homotopy type .
Homotopy invariant: A characteristic of a space that is preserved under homotopy equivalence of topological spaces . That is, if two spaces are homotopy equivalent, then they have the same characteristic. For example, connectivity , fundamental group , Euler characteristic are homotopy invariants.
Homotopy type: The homotopy equivalence class of topological spaces , that is, homotopy equivalent spaces are called spaces of the same homotopy type.
The border: 1. The relative boundary .; 2. The same as the edge of diversity .

D

Door space: A space in which any subset is either open or closed.
Colon: Topological space consisting of two points; there are three options for specifying a topology — a discrete topology forms a simple colon , an antidiscrete one forms a stuck colon , and a topology with an open set of one point makes a connected colon .
Strain retract: Subset $A$ ${\ displaystyle A}$ topological space $X$ ${\ displaystyle X}$ possessing the property that there is a homotopy of the identity mapping of space $\mathrm {id} _{X}$ ${\ displaystyle \ mathrm {id} _ {X}}$ in some mapping $X\to A$ ${\ displaystyle X \ to A}$ at which all points of the set $A$ ${\ displaystyle A}$ remain motionless .
Discrete topology: A topology in which any set is open .
Discrete set: A set, each point of which is isolated .

W

Closed set: A set that complements the open .
Closed Mapping: A mapping in which the image of any closed set is closed.
Short circuit: The smallest closed set containing this.

And

Induced Topology: Topology on a subset $A$ ${\ displaystyle A}$ topological space, open sets in which are considered the intersections of open sets of the ambient space with $A$ ${\ displaystyle A}$ .
Isolated Point Set: Point $a$ ${\ displaystyle a}$ called isolated for the set $A$ ${\ displaystyle A}$ topological space $X$ ${\ displaystyle X}$ if there is a neighborhood $O(a)$ ${\ displaystyle O (a)}$ such that $A\cap O(a)=a$ ${\ displaystyle A \ cap O (a) = a}$ .

To

Cardinal invariant: A topological invariant expressed by a cardinal number .
Baire Category: A characteristic of a topological space that takes one of two values; the first Baire category includes spaces that can be countably covered by nowhere dense subsets; other spaces belong to the second Baire category.
Compactification: Space compactification $X$ ${\ displaystyle X}$ is a couple $(Y,f)$ ${\ displaystyle (Y, f)}$ where $Y$ ${\ displaystyle Y}$ - compact space $f$ ${\ displaystyle f}$ - homeomorphic embedding of space $X$ ${\ displaystyle X}$ into space $Y$ ${\ displaystyle Y}$ , and $f(X)$ ${\ displaystyle f (X)}$ everywhere tight in $Y$ ${\ displaystyle Y}$ Space itself is also called compactification. $Y$ ${\ displaystyle Y}$ .
Compact display: A mapping of topological spaces whose inverse image of each point is compact .
Compact space: A topological space in any cover of which by open sets there is a finite subcover .
Point connectivity component: The maximum connected set containing this point.
Continuum: A connected compact Hausdorff topological space.
Cone over a topological space: For space $X$ ${\ displaystyle X}$ (called the base of the cone ) - space $\mathrm {C} X$ ${\ displaystyle \ mathrm {C} X}$ resulting from a work $X\times [0,\;1]$ ${\ displaystyle X \ times [0, \; 1]}$ contraction of subspace $X\times \{0\}$ ${\ displaystyle X \ times \ {0 \}}$ at one point called the vertex of the cone .

L

Lindelof space: A topological space in any covering of which by open sets there is a countable subcover.
Linearly connected space: The space in which any pair of points can be connected by a curve.
Locally compact space: The space in which any point has a compact neighborhood .
Locally finite family of subsets: Such a family of subsets of a topological space that every point of this space has a neighborhood intersecting only with a finite number of elements of this family.
Locally connected space: The space in which any point has a connected neighborhood .
Locally contractible space: The space in which any point has a contractible neighborhood .
Local homeomorphism: Display $f\colon X\to Y$ ${\ displaystyle f \ colon X \ to Y}$ topological spaces such that for each point $x\in X$ ${\ displaystyle x \ in X}$ there is a neighborhood $U_{x}$ ${\ displaystyle U_ {x}}$ which through $f$ ${\ displaystyle f}$ displayed in $Y$ ${\ displaystyle Y}$ homeomorphic. Sometimes a requirement is automatically included in the definition of a local homeomorphism $f(X)=Y$ ${\ displaystyle f (X) = Y}$ and, in addition, the mapping $f$ ${\ displaystyle f}$ supposed to be open.

M

Massive set: Subset $S$ ${\ displaystyle S}$ topological space $X$ ${\ displaystyle X}$ , which is the intersection of the countable number of open dense in $X$ ${\ displaystyle X}$ subsets. If each massive set is dense in $X$ ${\ displaystyle X}$ then $X$ ${\ displaystyle X}$ is a Baire space .
Metrizable space: A space homeomorphic to a complete metric space .
Metrizable space: A space homeomorphic to a metric space .
Manifold: Hausdorff topological space locally homeomorphic to Euclidean space .
Connected area: A domain of a linearly connected space whose fundamental group is not trivial.
Set of second category Baire: Any set that is not a set of the first Baire category .
Set of first category bera: A set that can be represented as a countable union of nowhere dense sets.
Set of type $F_{\sigma }$ ${\ displaystyle F _ {\ sigma}}$: A set that can be represented as a countable union of closed sets.
Set of type $G_{\delta }$ ${\ displaystyle G _ {\ delta}}$: A set that can be represented as a countable intersection of open sets.

H

Cover: Mapping linearly connected spaces $p:X\to Y$ ${\ displaystyle p: X \ to Y}$ at which at any point $y\in Y$ ${\ displaystyle y \ in Y}$ there is a neighborhood $U\subset Y$ ${\ displaystyle U \ subset Y}$ for which there is a homeomorphism $h:p^{-1}(U)\to U\times \Gamma$ ${\ displaystyle h: p ^ {- 1} (U) \ to U \ times \ Gamma}$ where $\Gamma$ ${\ displaystyle \ Gamma}$ - discrete space for which under $\pi :U\times \Gamma \to U$ ${\ displaystyle \ pi: U \ times \ Gamma \ to U}$ denotes a natural projection then $p|_{p^{-1}(U)}=\pi \circ h$ ${\ displaystyle p | _ {p ^ {- 1} (U)} = \ pi \ circ h}$ .
Hereditary property: A property of a topological space, such that if space has this property, then any subspace of it has this property. For example: metrizability and Hausdorff . If every subspace of space $X$ ${\ displaystyle X}$ possesses the property $P$ ${\ displaystyle P}$ then they say that $X$ ${\ displaystyle X}$ hereditarily possesses the property $P$ ${\ displaystyle P}$ . For example, they say that a topological space is hereditarily normal, hereditarily Lindelöf, hereditarily separable.
Continuous display: A mapping in which the inverse image of any open set is open.
Nowhere dense set: A set whose closure does not contain open sets (the closure has an empty interior).

Normal space

A topological space in which one-point sets are closed and any two closed disjoint sets have disjoint neighborhoods .

O

Region: An open connected subset of a topological space .
Simply connected space: A connected space , any map of a circle into which is homotopic to a constant map.
Neighborhood: An open neighborhood or set containing an open neighborhood .
Open neighborhood: For a point or set, an open set containing a given point or given set.
Open set: A set, each element of which is included in it together with a certain neighborhood, a concept used to define a topological space .
Open mapping: A mapping in which the image of any open set is open .
Open-closed set: A set that is both open and closed .
Open Closed Mapping: A mapping that is both open and closed .
Relative boundary: The intersection of the closure of a subset of a topological space with the closure of its complement. The border of the multitude $E$ ${\ displaystyle E}$ usually indicated $\partial E$ ${\ displaystyle \ partial E}$ .
Relative topology: Same as induced topology .
Relatively compact set: A subset of a topological space whose closure is compact. Also, such a set is called precompact .

N

Paracompact space: A topological space in which any open covering can contain a locally finite open covering (that is, such that for any point one can find a neighborhood intersecting with a finite number of elements of this covering).
Density of topological space: The minimum cardinalities of everywhere dense subsets of space.
Dense set: Set in a topological space $X$ ${\ displaystyle X}$ having a nonempty intersection with any neighborhood of an arbitrary point $x\in X$ ${\ displaystyle x \ in X}$ .
Subcover: To cover $\{V_{\alpha }\}$ ${\ displaystyle \ {V _ {\ alpha} \}}$ , $\alpha \in A$ ${\ displaystyle \ alpha \ in A}$ subcover is $\{V_{\beta }\}$ ${\ displaystyle \ {V _ {\ beta} \}}$ where $\beta \in B\subset A$ ${\ displaystyle \ beta \ in B \ subset A}$ , if a $\{V_{\beta }\}$ ${\ displaystyle \ {V _ {\ beta} \}}$ itself is a coating.
Subspace: A subset of a topological space equipped with an induced topology .
Coating: For a subset or space $X$ ${\ displaystyle X}$ Is a representation of it in the form of a union of sets $\{V_{\alpha }\}$ ${\ displaystyle \ {V _ {\ alpha} \}}$ , $\alpha \in A$ ${\ displaystyle \ alpha \ in A}$ more precisely, it is a set of sets $\{V_{\alpha }\}$ ${\ displaystyle \ {V _ {\ alpha} \}}$ , $\alpha \in A$ ${\ displaystyle \ alpha \ in A}$ such that $X\subset \bigcup _{\alpha \in A}V_{\alpha }$ ${\ displaystyle X \ subset \ bigcup _ {\ alpha \ in A} V _ {\ alpha}}$ . Most often, open coatings are considered, that is, they assume that everything $\{V_{\alpha }\}$ ${\ displaystyle \ {V _ {\ alpha} \}}$ are open sets.
Cech-complete space: Space $X$ ${\ displaystyle X}$ called Cech complete if compactification exists $(Y,f)$ ${\ displaystyle (Y, f)}$ of space $X$ ${\ displaystyle X}$ such that $f(X)$ ${\ displaystyle f (X)}$ is a set of type $G_{\delta }$ ${\ displaystyle G _ {\ delta}}$ in space $Y$ ${\ displaystyle Y}$ .
Ordinal Topology: Topology on an arbitrary ordered set $\langle X,\sqsubseteq \rangle$ ${\ displaystyle \ langle X, \ sqsubseteq \ rangle}$ introduced by a prebase from sets of the form $\{x\in X\mid x\sqsubseteq a,x\neq a\}$ ${\ displaystyle \ {x \ in X \ mid x \ sqsubseteq a, x \ neq a \}}$ and $\{x\in X\mid a\sqsubseteq x,x\neq a\}$ ${\ displaystyle \ {x \ in X \ mid a \ sqsubseteq x, x \ neq a \}}$ where $a$ ${\ displaystyle a}$ runs through all the elements $X$ ${\ displaystyle X}$ .
Pre-base: Family $Y$ ${\ displaystyle Y}$ open subsets of a topological space $X$ ${\ displaystyle X}$ such that the set of all sets that are the intersection of a finite number of elements $Y$ ${\ displaystyle Y}$ forms the base $X$ ${\ displaystyle X}$ .
Limit point: For a subset $A$ ${\ displaystyle A}$ topological space $X$ ${\ displaystyle X}$ - such a point $a\in X$ ${\ displaystyle a \ in X}$ that in any of its punctured neighborhoods with $A$ ${\ displaystyle A}$ there is at least one point from $A$ ${\ displaystyle A}$ .
Derived set: The set of all limit points .
Simple colon: A topological space of two points, in which both single-point sets are open.
Direct Alexandrova: Topological space over the Cartesian product of a well-ordered set and a real half-interval $A\times [0,1)$ ${\ displaystyle A \ times [0,1)}$ with ordinal topology under lexicographic ordering, is a normal Hausdorff non - metrizable space, an important counterexample in many topological considerations.
Suslin's Straight: Hypothetical (its existence independently of ZFC ) is a complete linearly ordered dense set that has some properties of the ordinary line but is not isomorphic to it.
The pseudo-character of a topological space: The supremum of pseudo- characters of a topological space at all points.
The pseudo-character of a topological space at a point: The minimum cardinalities of all families of neighborhoods of a point that give this point at the intersection.

P

Regular space: A topological space in which single-point sets are closed, and for any closed set and points not contained in it, their disjoint neighborhoods exist.
Retract: Retract of topological space $X$ ${\ displaystyle X}$ - subspace $A$ ${\ displaystyle A}$ of this space for which retraction exists $X$ ${\ displaystyle X}$ on $A$ ${\ displaystyle A}$ .
Retraction: Retraction - continuous mapping from a topological space $X$ ${\ displaystyle X}$ to subspace $A$ ${\ displaystyle A}$ of this space, identical on $A$ ${\ displaystyle A}$ .

C

Connected colon: A topological space of two points, only one of the one-point sets in which is open.
Connected space: A space that cannot be divided into two nonempty disjoint closed sets.
Separable space: A topological space in which there is a countable everywhere dense set .
Net weight of a topological space: The minimum capacity of all networks of space.
Network: Network of topological space $X$ ${\ displaystyle X}$ is a family $N$ ${\ displaystyle N}$ subsets of space $X$ ${\ displaystyle X}$ such that for any point $x$ ${\ displaystyle x}$ and any of its surroundings $U$ ${\ displaystyle U}$ , exists $V\in N$ ${\ displaystyle V \ in N}$ such that $x\in V\subset U$ ${\ displaystyle x \ in V \ subset U}$ .
Stuck colon: Two-point antidiscrete topological space.
Topological space spread: The supremum of cardinalities of all discrete subspaces.
Contractible space: A space homotopy equivalent to a point.
Sum of topological spaces: The sum of a family of topological spaces $\{A_{s}\}_{s\in S}$ ${\ displaystyle \ {A_ {s} \} _ {s \ in S}}$ called disjoint union $\coprod _{s\in S}A_{s}$ ${\ displaystyle \ coprod _ {s \ in S} A_ {s}}$ of these topological spaces as sets with a topology consisting of all sets of the form $\coprod _{s\in S}U_{s}$ ${\ displaystyle \ coprod _ {s \ in S} U_ {s}}$ where each $U_{s}$ ${\ displaystyle U_ {s}}$ open in $A_{s}$ ${\ displaystyle A_ {s}}$ . Designated $\bigoplus _{s\in S}A_{s}$ ${\ displaystyle \ bigoplus _ {s \ in S} A_ {s}}$ .

T

The tightness of topological space: The supremum is the tightness of the topological space at all points.
The tightness of the topological space at the point: The tightness of topological space $X$ ${\ displaystyle X}$ at the point $x$ ${\ displaystyle x}$ called the smallest cardinal $\alpha$ ${\ displaystyle \ alpha}$ for which if $x\in {\bar {A}}$ ${\ displaystyle x \ in {\ bar {A}}}$ then exists $B\subset A$ ${\ displaystyle B \ subset A}$ power no more $\alpha$ ${\ displaystyle \ alpha}$ such that $x\in {\bar {B}}$ ${\ displaystyle x \ in {\ bar {B}}}$ .
Tikhonov space: A topological space in which one-point sets are closed for any point $x$ ${\ displaystyle x}$ and any closed set $F$ ${\ displaystyle F}$ not containing a point $x$ ${\ displaystyle x}$ there is a continuous real function equal to $0$ ${\ displaystyle 0}$ on set $F$ ${\ displaystyle F}$ and $one$ ${\ displaystyle 1}$ at the point $x$ ${\ displaystyle x}$ .
Topological invariant: A characteristic of the space that is preserved by homeomorphism . That is, if two spaces are homeomorphic, then they have the same invariant characteristic. For example, topological invariants are: compactness , connectedness , fundamental group , Euler characteristic .
Topologically Injective Mapping: A continuous mapping that implements a homeomorphism between the domain of definition and its full image.
Topological space: A set with a given topology , that is, it is determined which subsets of it are open .
Topology: Set subset family $X$ ${\ displaystyle X}$ , containing an arbitrary union and a finite intersection of its elements, as well as an empty set and itself $X$ ${\ displaystyle X}$ . Elements of a family are called open sets . Also, the topology can be introduced through the base , as a family consisting of all arbitrary associations of base elements.
Compact convergence topology: A topology defined on the set of continuous real functions defined by the family of prenorms $p_{n}(x)=\sup _{-n\leqslant t\leqslant n}|x(t)|,\;n\in \mathbb {N}$ ${\ displaystyle p_ {n} (x) = \ sup _ {- n \ leqslant t \ leqslant n} | x (t) |, \; n \ in \ mathbb {N}}$ , is called the compact convergence topology.
Point Convergence Topology: The topology defined on the set $C(X,Y)$ ${\ displaystyle C (X, Y)}$ continuous functions from a topological space $X$ ${\ displaystyle X}$ into the topological space $Y$ ${\ displaystyle Y}$ whose base are all sets of the form $\{f:f(x_{1})\in U_{1},f(x_{2})\in U_{2},\dots ,f(x_{n})\in U_{n}\},$ ${\ displaystyle \ {f: f (x_ {1}) \ in U_ {1}, f (x_ {2}) \ in U_ {2}, \ dots, f (x_ {n}) \ in U_ {n } \},}$ Where $x_{1},x_{2},\dots x_{n}$ ${\ displaystyle x_ {1}, x_ {2}, \ dots x_ {n}}$ - points from $X,U_{1},U_{2},\dots U_{n}$ ${\ displaystyle X, U_ {1}, U_ {2}, \ dots U_ {n}}$ - open sets from $Y$ ${\ displaystyle Y}$ is called the pointwise convergence topology. Lots of $C(X,Y)$ ${\ displaystyle C (X, Y)}$ with such a topology is denoted $C_{p}(X,Y)$ ${\ displaystyle C_ {p} (X, Y)}$ .
Topology of uniform convergence: Let on the vector space $L(K)$ ${\ displaystyle L (K)}$ continuous functions $f$ ${\ displaystyle f}$ on a compact topological space $K$ ${\ displaystyle K}$ defined norm $\|f\|=\sup _{x\in K}|f(x)|$ ${\ displaystyle \ | f \ | = \ sup _ {x \ in K} | f (x) |}$ . The topology generated by such a metric is called the topology of uniform convergence.
Scott Topology: A topology over a complete partially ordered set in which upper sets are considered open, inaccessible to direct connections.
Accumulation point: Same as limit point .
Full accumulation point: For many $M$ ${\ displaystyle M}$ - point $x\in M$ ${\ displaystyle x \ in M}$ in topological space $X$ ${\ displaystyle X}$ such that the intersection $M$ ${\ displaystyle M}$ with any neighborhood $x$ ${\ displaystyle x}$ has the same power as the whole set $M$ ${\ displaystyle M}$ .
Touch point: For many $M$ ${\ displaystyle M}$ Is a point, any neighborhood of which contains at least one point from $M$ ${\ displaystyle M}$ . The set of all touch points coincides with the closure. ${\overline {M}}$ ${\ displaystyle {\ overline {M}}}$ .
Trivial topology: Same as Discrete Topology

U

Seal: Continuous bijection .

Factor space: A topological space on the set of equivalence classes: for a topological space $X$ ${\ displaystyle X}$ and equivalence relations $\sim$ ${\ displaystyle \ sim}$ topology on a factor set $X/\!\sim$ ${\ displaystyle X / \! \ sim}$ is introduced by the definition of open sets as the family of all sets whose inverse image is open in $X$ ${\ displaystyle X}$ in factor display (which assigns an element $x\in X$ ${\ displaystyle x \ in X}$ its equivalence class $[x]_{\sim }=\{y\in X\mid x\sim y\}$ ${\ displaystyle [x] _ {\ sim} = \ {y \ in X \ mid x \ sim y \}}$ ).
The fundamental system of neighborhoods: The fundamental system of neighborhoods of a point $x$ ${\ displaystyle x}$ is a family $B$ ${\ displaystyle B}$ neighborhood points $x$ ${\ displaystyle x}$ such that for any neighborhood $U$ ${\ displaystyle U}$ points $x$ ${\ displaystyle x}$ exists $V\in B$ ${\ displaystyle V \ in B}$ such that $V\subset U$ ${\ displaystyle V \ subset U}$ .

X

The nature of the topological space: The supremum of characters of a topological space at all points.
The nature of the topological space at the point: The minimum power of all fundamental systems of neighborhoods of this point.
Hausdorff space: A topological space, any two different points of which have disjoint neighborhoods .

C

Cylinder over topological space: For space $X$ ${\ displaystyle X}$ - space $\mathrm {Z} X$ ${\ displaystyle \ mathrm {Z} X}$ being built as a work $X\times [0,\;1]$ ${\ displaystyle X \ times [0, \; 1]}$ .
Display cylinder: To display $f:X\to Y$ ${\ displaystyle f: X \ to Y}$ - factor space $\mathrm {Z} _{f}$ ${\ displaystyle \ mathrm {Z} _ {f}}$ constructed from the amount $X\times [0,\;1]$ ${\ displaystyle X \ times [0, \; 1]}$ and $Y$ ${\ displaystyle Y}$ point identification $(x,1)\in X\times [0,\;1]$ ${\ displaystyle (x, 1) \ in X \ times [0, \; 1]}$ with dot $f(x)\in Y$ ${\ displaystyle f (x) \ in Y}$ for all $x\in X$ ${\ displaystyle x \ in X}$ .

H

Lindelof number of a topological space: Smallest cardinal $\alpha$ ${\ displaystyle \ alpha}$ such that it is possible to extract a subcoating from any open coating, with no more power $\alpha$ ${\ displaystyle \ alpha}$ .
Suslin number of a topological space: The supremum of cardinalities of families of disjoint nonempty open sets.

E

The extent of the topological space

The supremum of powers of all closed discrete subsets.

Literature

Bourbaki, N. Elements of mathematics. General topology. The main structure. - M .: Science, 1968.
Aleksandrov, P. S. Introduction to set theory and general topology. - M .: SIITL, 1948.
Kelly, J.L. General Topology. - M .: Science, 1968.
Viro, O. Ya., Ivanov, O.A., Kharlamov, V.M., Netsvetaev, N. Yu. Problem textbook on topology .
Engelking, R. General Topology. - M .: Mir , 1986 .-- 752 p.

Glossary of general topology

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