homeomorphism

American  

[hoh-mee-uh-mawr-fiz-uhm] / ˌhoʊ mi əˈmɔr fɪz əm /

noun

1. similarity in crystalline form but not necessarily in chemical composition.

2. Mathematics.  a function between two topological spaces that is continuous, one-to-one, and onto, and the inverse of which is continuous.

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homeomorphism British  

/ ˌhəʊmɪəˈmɔːfɪzəm /

noun

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

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homeomorphism Scientific  

/ hō′mē-ə-môr′fĭz′əm /

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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Other Word Forms

• homeomorphic adjective
• homeomorphous adjective

Etymology

Origin of homeomorphism

First recorded in 1850–55; homeomorph + -ism

Example Sentences

Homeomorphism is one version of equivalence.

From Scientific American

We can see that these spaces don’t have this stronger ambient homeomorphism by looking at what happens around them.

From Scientific American

This is called ambient homeomorphism.

From Scientific American

We could request this continuous function from one mathematical object to another with a continuous inverse also be a homeomorphism of the ambient space around the two objects, which basically mean it doesn't just have to be nice to the mathematical object but to the entire universe the object lives in.

From Scientific American