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...bsolute G_δ'', that is, a [[G-delta set|G_δ]] in every topological space in which it can be embedded.

A subset of a topological space that is a countable intersection of open sets.

A set in a topological space with no isolated points, so that all its points are limit points of itself.

A point of a topological space which is not contained in any proper closed subset; a point satisfying no s

'''Countability axioms in topology''' are properties that a [[topological space]] may satisfy which refer to the [[countable set|countability]] of certain

Topological space together with commutative rings for all its open sets, which arises from 'g

...a [[topological space]] ''X'' is the set union of ''A'' and ''all'' its [[topological space#Some topological notions|limit points]] in ''X''. It is usually denoted by

A point which cannot be separated from a given subset of a topological space; all neighbourhoods of the points intersect the set.

In a topological space, a set containing a given point in its interior, expressing the idea of poi

{{r|Topological space}}

===Function on a topological space=== ...math>U_x</math> and <math>U_y</math> can be taken to be, respectively, a [[topological space#Some topological notions|neighbourhood]] of ''x'' and a neighbourhood of <m

In [[mathematics]], a '''compact space''' is a [[topological space]] for which every covering of that space by a collection of [[open set]]s h A subset of a topological space is compact if it is compact with respect to the [[subspace topology]].

{{r|Topological space}}

...where a function does not take some specific value, such as zero. (2) In a topological space, the closure of that set.

...e on a category C which makes the objects of C act like the open sets of a topological space.

{{r|Topological space}}

In [[topology]], a '''connected space''' is a [[topological space]] in which there is no (non-trivial) [[subset]] which is simultaneously [[o A '''connected component''' of a topological space is a maximal connected subset: that is, a subspace ''C'' such that ''C'' is

A function that maps one topological space to another with the property that it is bijective and both the function and

In [[topology]], a '''Noetherian space''' is a [[topological space]] satisfying the [[descending chain condition]] on [[closed set]]s.

In [[topology]], a '''door space''' is a [[topological space]] in which each [[subset]] is [[open set|open]] or [[closed set|closed]] or