homotopy equivalence
Continuous deformation correspondence
Homotopy equivalence is a relationship between two topological spaces that can be continuously deformed into each other.
Two spaces are homotopy equivalent if there exist continuous maps between them that, when composed, can be continuously deformed back to the identity map.
A coffee mug and a donut are homotopy equivalent—both have one hole.
The concept relaxes the stricter notion of homeomorphism, grouping spaces by their essential topological features rather than exact shape.
- contractibleAble to be shrunk
- homologyStructural similarity through descent
- manifoldMany and various
- continuousWithout pause or gap
- pathRoute for traveling
mapping · deformation · sphere · retract · torus · suspension · invariant · loop · data analysis · connectedness · chain · compactness · category · topological · graph theory · bundle · topology · topology
- homotopy