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 $\left({X, \tau}\right)$
Morphisms: Continuous Mapping
Composition: Standard composition of mappings
Identity morphisms: $\operatorname{id}_{\left({X, \tau}\right)} := \operatorname{id}_X$, the identity mapping on $X$


Also see