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...tics]], a set <math>A \subset X</math>, where <math>(X,O)</math> is some [[topological space]], is said to be closed if <math>X-A=\{x \in X \mid x \notin A\}</math>, th

#A standard topological space <math>X</math> becomes a category <math>op(X)</math> when you regard the op

Let ''X'' be a [[topological space]]. A subset <math>\scriptstyle A \subset X</math> is said to be '''dense'''

In [[general topology]], a generic point of a [[topological space]] ''X'' is a point ''x'' such that the closure of the [[singleton]] set {''

...'s Theorem]]: The product of a family of non-empty [[compact space|compact topological space]]s is compact in the [[product topology]].

...erating properties of an object called 'open set'. For this approach see [[topological space]].

In [[mathematics]], the '''interior''' of a subset ''A'' of a [[topological space]] ''X'' is the [[union]] of all [[open set]]s in ''X'' that are [[subset]]s

We say that a [[topological space]] ''X'' is

#The category of [[sheaves]] on a topological space <math>X</math> with values in an abelian category is again an abelian categ

...se is wrong: a homeomorphism may distort distances. In terms of Bourbaki, "topological space" is an '''underlying''' structure of the "Euclidean space" structure. Simil ...se, the species of compact topological space is richer than the species of topological space.

...ology]], an '''open map''' is a [[function (mathematics)|function]] on a [[topological space]] which maps every [[open set]] in the domain to an open set in the image.

In [[topology]] a surface is defined as a topological space such that

In a [[topological space]] <math>(X,\mathcal{T})</math>, the [[neighbourhood]]s of a point ''x''

A '''scheme''' <math>(X,\mathcal{O}_X)</math> consists of a topological space <math>X</math> together with a sheaf <math>\mathcal{O}_X</math> of rings (c

...which is equipped with the binary operation of "+" ([[addition]]) and a [[topological space|topology]], for example the algebra of the real numbers with the standard E

...or mathematical analysis, the notion seems less fundamental than that of a topological space. The notion of uniformity is auxiliary rather than an object to be studied * topology (as a family of open sets), [[topological space]];

...al space#Some topological notions|connected]] and [[simply connected]]), [[topological space#Some topological notions|connected]] metric space of [[dimension]] 1, and a

...of a [[function space]] can be illustrated using a [[vector space]] or a [[topological space]] that introduce interpretations of the 'elements' of the conceptualization

...eave much more freedom; every subset of (say) the plane is an example of a topological space, be it connected or not, compact or not, be it a curve, a domain, a fractal

*[[user: Jitse Niesen|Jitse]] was [[Topological space|spaced out]].