\begin{definition}[Definition:Category of Topological Spaces]
The '''category of topological spaces''', denoted $\mathbf{Top}$, is defined as follows:
{{DefineCategory
| ob = Topological Spaces $\struct {X, \tau}$
| mor = Continuous Mapping
| comp = Standard composition of mappings
| id = $\operatorname{id}_{\struct {X, \tau} } := \operatorname{id}_X$, the identity mapping on $X$
}}
\end{definition}