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A topological space with a countable dense subset.

A topological space in which every sequence has a convergent subsequence.

A set in a topological space whose closure has empty interior.

#REDIRECT [[Topological space#Bases and sub-bases]]

#REDIRECT [[Topological space#Bases and sub-bases]]

A topological space in which every irreducible closed set has a unique generic point.

A property that describes how good points in a topological space can be distinguished.

A topological space in which there is no non-trivial subset which is both open and closed.

Function on a directed set into a topological space which generalises the notion of sequence.

In [[general topology]], a '''G_δ set''' is a [[subset]] of a [[topological space]] which is a [[countability|countable]] [[intersection]] of [[open set]]s. A '''G_δ space''' is a topological space in which every closed set is a G_δ set. A [[normal space]] whic

Axioms for a topological space which specify how well separated points and closed sets are by open sets.

Topological space with additional structure which is used to define uniform properties such a

An assignment of open sets to a subset of a topological space.

The union of all open sets contained within a given subset of a topological space.

The finest topology on the image set that makes a surjective map from a topological space continuous.

A set that belongs to the σ-algebra generated by the open sets of a topological space.

{{r|Topological space}}

The Cantor set may be considered a [[topological space]], [[homeomorphism|homeomorphic]] to a product of [[countable set|countably As a topological space, the Cantor set is [[uncountable set|uncountable]], [[compact space|compact

For a topological space this generalises the notion of "point at infinity" of the real line or plan

...to the [[sigma algebra|&sigma;-algebra]] generated by the open sets of a [[topological space]]. Thus, every open set is a Borel set, as are countable unions of open set ...math>O</math> are the open sets of <math>X</math> (or, equivalently, the [[topological space|topology]] of <math>X</math>). Then <math>A \subset X </math> is a Borel se