Definition:Category of Topological Spaces

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Definition

The category of topological spaces, denoted $\mathbf{Top}$, is defined as follows:

Objects:         Topological Spaces $\struct {X, \tau}$
Morphisms: Continuous Mapping
Composition: Standard composition of mappings
Identity morphisms: $\operatorname{id}_{\struct {X, \tau} } := \operatorname{id}_X$, the identity mapping on $X$


Also see