There are two possible definitions:

- 1. Possessing similarity of form,
- 2. Continuous, One-to-One, Onto, and having a continuous inverse.

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.

In Category Theory terms, homeomorphisms
are Isomorphisms in the Category of Topological Spaces and
continuous maps.

*See also *Homomorphic, Polish Space

© 1996-9 *Eric W. Weisstein *

1999-05-25