Category of topological spaces - Revision history

InfernalAtom683 at 14:58, 10 April 2026

2026-04-10T14:58:34Z

← Older revision		Revision as of 22:58, 10 April 2026
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	* [[Category of sets]]		* [[Category of sets]]
	* [[Category of groups]]		* [[Category of groups]]

			== Terminology ==

			{{Terminology_table\|
			{{Terminology_table/row \| category of topological spaces \| catégorie des espaces topologiques \| Kategorie der topologischen Räume \| 拓扑空间范畴 \| 拓撲空間範疇 \| 位相空間の圏 }}
			{{Terminology_table/row \| topological space \| espace topologique \| topologischer Raum \| 拓扑空间 \| 拓撲空間 \| 位相空間 }}
			{{Terminology_table/row \| continuous function \| fonction continue \| stetige Funktion \| 连续函数 \| 連續函數 \| 連続関数 }}
			{{Terminology_table/row \| category of Hausdorff spaces \| catégorie des espaces de Hausdorff \| Kategorie der Hausdorff‑Räume \| Hausdorff 空间范畴 \| Hausdorff 空間範疇 \| ハウスドルフ空間の圏 }}
			{{Terminology_table/row \| category of compact spaces \| catégorie des espaces compacts \| Kategorie der kompakten Räume \| 紧空间范畴 \| 緊空間範疇 \| コンパクト空間の圏 }}
			{{Terminology_table/row \| category of pointed topological spaces \| catégorie des espaces pointés \| Kategorie der punktierten topologischen Räume \| 带点拓扑空间范畴 \| 帶點拓撲空間範疇 \| 点付き位相空間の圏 }}
			{{Terminology_table/row \| category of CW complexes \| catégorie des complexes CW \| Kategorie der CW‑Komplexe \| CW复形范畴 \| CW複形範疇 \| CW複体の圏 }}
			}}

InfernalAtom683 at 03:26, 6 April 2026

2026-04-06T03:26:24Z

← Older revision		Revision as of 11:26, 6 April 2026
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	The category <math>\mathsf{Top}</math> consists of:		The category <math>\mathsf{Top}</math> consists of:

	* <math>\operatorname{ob}(\mathsf{Top})</math> ~~consists~~ of all topological spaces,		* <math>\operatorname{ob}(\mathsf{Top})</math> is the class of all topological spaces;
	* <math>\operatorname{mor}(\mathsf{Top})</math> ~~consists~~ of all ~~continuos~~ functions.		* <math>\operatorname{mor}(\mathsf{Top})</math> is the class of all continuous functions between topological spaces;
			* The composition operation <math>\circ</math> is given by the composition of ordinary functions.

	== Subcategories ==		== Subcategories ==
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	* <math>\mathsf{Top}_{*}</math>, [[category of pointed topological spaces]];		* <math>\mathsf{Top}_{*}</math>, [[category of pointed topological spaces]];
	* <math>\mathsf{CW}</math>, [[category of CW complexes]] or cell complexes.		* <math>\mathsf{CW}</math>, [[category of CW complexes]] or cell complexes.

			== See also ==

			* [[Category theory]]
			* [[Morphism]]
			* [[Category of sets]]
			* [[Category of groups]]

InfernalAtom683: Created page with "The '''category of topological spaces''', denoted $\mathsf{Top}$ or $\mathbf{Top}$ , is the category whose objects are topological spaces and whose morphisms are continuous functions. == Definition == The category $\mathsf{Top}$ consists of: * $\operatorname{ob}(\mathsf{Top})$ consists of all topological spaces, * $\operatorname{mor}(\mathsf{Top})$ consi..."

2026-03-22T12:57:06Z

Created page with "The '''category of topological spaces''', denoted <math>\mathsf{Top}</math> or <math>\mathbf{Top}</math>, is the category whose objects are topological spaces and whose morphisms are continuous functions. == Definition == The category <math>\mathsf{Top}</math> consists of: * <math>\operatorname{ob}(\mathsf{Top})</math> consists of all topological spaces, * <math>\operatorname{mor}(\mathsf{Top})</math> consi..."

New page

The '''category of topological spaces''', denoted <math>\mathsf{Top}</math> or <math>\mathbf{Top}</math>, is the [[category]] whose objects are [[Topological space|topological spaces]] and whose [[Morphism|morphisms]] are [[Continuous function|continuous functions]].

== Definition ==
The category <math>\mathsf{Top}</math> consists of:

* <math>\operatorname{ob}(\mathsf{Top})</math> consists of all topological spaces,
* <math>\operatorname{mor}(\mathsf{Top})</math> consists of all continuos functions.

== Subcategories ==
Several important subcategories of <math>\mathsf{Top}</math> arise by restricting objects:

* <math>\mathsf{Haus}</math>, [[category of Hausdorff spaces]];
* <math>\mathsf{Comp}</math>, [[category of Compact spaces]];

* <math>\mathsf{Top}_{*}</math>, [[category of pointed topological spaces]];
* <math>\mathsf{CW}</math>, [[category of CW complexes]] or cell complexes.