homeomorphism
A homeomorphism of topological spaces
is a continuous
, bijective
map such that is also continuous. We also say that two spaces are homeomorphic if such a map exists.
If two topological spaces are homeomorphic, they are topologically equivalent — using the techniques of topology, there is no way of distinguishing one space from the other.
An autohomeomorphism (also known as a self-homeomorphism) is a homeomorphism from a topological space to itself.
| Title | homeomorphism |
| Canonical name | Homeomorphism |
| Date of creation | 2013-03-22 11:59:35 |
| Last modified on | 2013-03-22 11:59:35 |
| Owner | rspuzio (6075) |
| Last modified by | rspuzio (6075) |
| Numerical id | 16 |
| Author | rspuzio (6075) |
| Entry type | Definition |
| Classification | msc 54C05 |
| Synonym | topological equivalence |
| Synonym | topologically equivalent |
| Related topic | Homeotopy |
| Related topic | CrosscapSlide |
| Related topic | AlexanderTrick |
| Related topic | GroupoidCategory |
| Defines | homeomorphic |
| Defines | autohomeomorphism |
| Defines | auto-homeomorphism |
| Defines | self-homeomorphism |