Category of topological spaces

The category of topological spaces, denoted or , is the category whose objects are topological spaces and whose morphisms are continuous functions.

Definition

The category consists of:

• consists of all topological spaces,
• consists of all continuos functions.

Subcategories

Several important subcategories of arise by restricting objects:

• , category of Hausdorff spaces;
• , category of Compact spaces;

• , category of pointed topological spaces;
• , category of CW complexes or cell complexes.