In topology, two surfaces are homeomorphic if they share a homeomorphism; that is, if you can stretch one into the other with out breaking the surface (if you can do that without passing it through itself, they're not only homeomorphic but isotopic). Occasionally spelled "homoeomorphic" or "homoiomorphic" (mostly by the same british people who gave us "colour", "flavour", and "connexion"). The word "homomorphic" (see homomorphism) has a subtly different meaning that applies to set theory and other areas of math, as well as a different meaning in almost every branch of biology (botany, zoology, cytology, entomology...). The word "homeomorphous" is used in crystallography and paleontology, but the word "homomorphous" is more general and simply means "of the same or similar form".

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