from The American Heritage® Dictionary of the English Language, 4th Edition
- n. Chemistry A close similarity in the crystal forms of unlike compounds.
- n. Mathematics A continuous bijection between two figures whose inverse is also continuous.
from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. a continuous bijection from one topological space to another, with continuous inverse.
- n. a similarity in the crystal structure of unrelated compounds
from the GNU version of the Collaborative International Dictionary of English
- n. A near similarity of crystalline forms between unlike chemical compounds. See isomorphism.
from The Century Dictionary and Cyclopedia
- n. Similarity in crystalline form, but not necessarily in chemical composition.
- n. Same as isomorphism.
- n. Also homeomorphism.
A homeomorphism is, essentially, a one-to-one correspondence (see any maths site for details).
One is that it is a homeomorphism invariant: if two spaces are homeomorphic, then they have the same fundamental group.
The topology on the countable product of the two-point space '' D '' is induced by the metric The Cantor set may be embedded in the unit interval by the map which is a homeomorphism onto the subset of the unit interval obtained by iteratively deleting the middle third of each interval compact.
The Cantor set is [[homeomorphism | homeomorphic]] to a product of [[countable set | countably]] many copies of a two-point space with the [[discrete metric]].
While the existence of a homeomorphism between manifolds demonstrates the existence of a diffeomorphism between them if they are of dimension it is possible to construct objects which are homeomorphic and not diffeomorphic - such objects are called "exotic