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:

• is the class of all topological spaces;
• is the class of all continuous functions between topological spaces;
• The composition operation is given by the composition of ordinary 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.

See also

• Category theory
• Morphism
• Category of sets
• Category of groups