G -sets are nothing but functors from this category to Set The category of all directed graphs is cartesian closed; this is a functor category as e...

Subcategory Faithful functor Full functor Forgetful functor Yoneda lemma Representable functor Functor category Adjoint functors Galois connection ...

Final topology - Wikipedia, the free encyclopedia Final topology From Wikipedia, the free encyclopedia Jump to: navigation , search In general topo...

T 0 spaces is T 0 Every product of T 1 spaces is T 1 Every product of Hausdorff spaces is Hausdorff [1] Every product of regular spaces is regular ...

Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of al...

The smash product of any pointed space X with a 0-sphere is homeomorphic to X . The smash product of two circles is a quotient of the torus homeomo...

Set (with the monoidal structure induced by the cartesian product) is a monoid in the usual sense. A monoid object in Top (with the monoidal struct...

For non first-countable spaces, sequential continuity might be strictly weaker than continuity. (The spaces for which the two properties are equiva...

Preservation of topological properties every disjoint union of discrete spaces is discrete Separation every disjoint union of T 0 spaces is T 0 eve...

Complete algebraic variety - Wikipedia, the free encyclopedia Complete algebraic variety From Wikipedia, the free encyclopedia   (Redirected from C...

Equivalently, it is a relatively open subset of its closure. Locally compact A space is locally compact if every point has a local base consisting ...

Alexandrov spaces can be viewed as a generalization of finite topological spaces . Contents 1 Characterizations of Alexandrov topologies 2 Duality ...