homeomorphism (redirected from Topological equivalence)

ho·me·o·mor·phism  (hm--môrfzm)

n.

1. Chemistry A close similarity in the crystal forms of unlike compounds.

2. Mathematics A continuous bijection between two figures whose inverse is also continuous.

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home·o·morphous adj.

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homeomorphism, homoeomorphism [ˌhəʊmɪəˈmɔːfɪzəm]

n

1. (Chemistry) the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition

2. (Mathematics) Maths a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces

homeomorphic , homeomorphous, homoeomorphic, homoeomorphous adj

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homeomorphism  (hm--môrfzm)

1. A close similarity in the crystal forms of unlike compounds.

2. A one-to-one correspondence between the points of two geometric figures such that open sets in the first geometric figure correspond to open sets in the second figure and conversely. If one figure can be transformed into another without tearing or folding, there exists a homeomorphism between them. Topological properties are defined on the basis of homeomorphisms.

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homeomorphism

the similarity of the crystalline forms of substances that have different chemical compositions. — homeomorphous, adj.

See also: Physics