American Heritage® Dictionary of the English Language, Fourth 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.
Century Dictionary and Cyclopedia
- n. Similarity in crystalline form, but not necessarily in chemical composition.
- n. Same as isomorphism.
- n. Also homeomorphism.
- n. topology a continuous bijection from one topological space to another, with continuous inverse.
- n. chemistry a similarity in the crystal structure of unrelated compounds
GNU Webster's 1913
- n. A near similarity of crystalline forms between unlike chemical compounds. See isomorphism.
- homeo- + -morphism (Wiktionary)
“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”
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