Topological Spaces

class sage.categories.topological_spaces.TopologicalSpaces(category, *args)

Bases: sage.categories.topological_spaces.TopologicalSpacesCategory

The category of topological spaces.

EXAMPLES:

sage: Sets().Topological()
Category of topological spaces
sage: Sets().Topological().super_categories()
[Category of sets]

The category of topological spaces defines the topological structure, which shall be preserved by morphisms:

sage: Sets().Topological().additional_structure()
Category of topological spaces
class Compact(base_category)

Bases: sage.categories.category_with_axiom.CategoryWithAxiom

The category of compact topological spaces.

class TopologicalSpaces.Connected(base_category)

Bases: sage.categories.category_with_axiom.CategoryWithAxiom

The category of connected topological spaces.

class TopologicalSpaces.SubcategoryMethods
Compact()

Return the subcategory of the compact objects of self.

EXAMPLES:

sage: Sets().Topological().Compact()
Category of compact topological spaces
Connected()

Return the full subcategory of the connected objects of self.

EXAMPLES:

sage: Sets().Topological().Connected()
Category of connected topological spaces
class sage.categories.topological_spaces.TopologicalSpacesCategory(category, *args)

Bases: sage.categories.covariant_functorial_construction.RegressiveCovariantConstructionCategory