# Category:Category of Topological Spaces

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 $X$