|homeomorphism or homoeomorphism (ˌhəʊmɪəˈmɔːfɪzəm)|
|1.||the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition|
|2.||maths a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces|
|homoeomorphism or homoeomorphism|
|homeo'morphic or homoeomorphism|
|homeo'morphous or homoeomorphism|
|homoeo'morphic or homoeomorphism|
|homoeo'morphous or homoeomorphism|
|homeomorphism (hō'mē-ə-môr'fĭz'əm) Pronunciation Key
in mathematics, a correspondence between two figures or surfaces or other geometrical objects, defined by a one-to-one mapping that is continuous in both directions. The vertical projection shown in the sets up such a one-to-one correspondence between the straight segment x and the curved interval y. If x and y are topologically equivalent, there is a function h:xy such that h is continuous, h is onto (each point of y corresponds to a point of x), h is one-to-one, and the inverse function, h1, is continuous. Thus h is called a homeomorphism.
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