There are two possible definitions:
The most common meaning is possessing intrinsic topological equivalence. Two objects are homeomorphic if they can be
deformed into each other by a continuous, invertible mapping. Homeomorphism ignores the space in which surfaces are
embedded, so the deformation can be completed in a higher dimensional space than the surface was originally embedded.
Mirror Images are homeomorphic, as are Möbius Strip with an Even number of half-twists, and
Möbius Strip with an Odd number of half-twists.
- 1. Possessing similarity of form,
- 2. Continuous, One-to-One, Onto, and having a continuous inverse.
In Category Theory terms, homeomorphisms
are Isomorphisms in the Category of Topological Spaces and
See also Homomorphic, Polish Space
© 1996-9 Eric W. Weisstein