Condensation point

Let the set${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">X</span></span>}}$ {\ displaystyle X} , lies in topological space . A point in any neighborhood of which contains an uncountable set of points of the set${\displaystyle \mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">X</span></span>}}$ {\ displaystyle X} called the condensation point .

• The set of condensation points of any set is closed
  • Moreover, if it is non-empty, then it is a perfect set and has the power of the continuum .

• Limit point