homeomorphism

ho·me·o·mor·phism

H0251500 (hō′mē-ə-môr′fĭz′əm)n.1. Chemistry A close similarity in the crystal forms of unlike compounds.2. Mathematics A continuous bijection between two topological spaces whose inverse is also continuous.

ho′me·o·mor′phic adj.

homeomorphism

(ˌhəʊmɪəˈmɔːfɪzəm) or

homoeomorphism

n1. (Chemistry) the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition2. (Mathematics) maths a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces ˌhomeoˈmorphic, ˌhomeoˈmorphous, ˌhomoeoˈmorphic, ˌhomoeoˈmorphous adj

ho•me•o•mor•phism

(ˌhoʊ mi əˈmɔr fɪz əm)

n. a mathematical function between two topological spaces that is continuous, one-to-one, and onto, and the inverse of which is continuous. [1850–55] ho`me•o•mor′phic, ho`me•o•mor′phous, adj.

homeomorphism

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

Translations

Homeomorphism

homeomorphism

[¦hō·mē·ə¦mȯr‚fiz·əm] (mathematics) A continuous map between topological spaces which is one-to-one, onto, and its inverse function is continuous. Also known as bicontinuous function; topological mapping.

Homeomorphism

one of the basic concepts of topology. Two figures (more precisely, two topological spaces) are said to be homeomorphic if there exists a one-to-one continuous mapping of any one onto the other, for which the inverse mapping is also continuous. In this case, the mapping itself is called a homeomorphism. For example, any circle is homeomorphic to any square; any two segments are homeomorphic, but a segment is not homeomorphic to a circle or a line. A line is homeomorphic to any interval (that is, a segment without end points). The concept of homeomorphism is the basis for defining the extremely important concept of a topological property. Specifically, a property of a figure F is said to be topological if it is found in all figures homeomorphic to F. Examples of topological properties are compactness and connectedness.

A. V. ARKHANGEL’SKII

单词	homeomorphism
释义	homeomorphism ho·me·o·mor·phism H0251500 (hō′mē-ə-môr′fĭz′əm)n.1. Chemistry A close similarity in the crystal forms of unlike compounds.2. Mathematics A continuous bijection between two topological spaces whose inverse is also continuous. ho′me·o·mor′phic adj. homeomorphism (ˌhəʊmɪəˈmɔːfɪzəm) or homoeomorphism n1. (Chemistry) the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition2. (Mathematics) maths a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces ˌhomeoˈmorphic, ˌhomeoˈmorphous, ˌhomoeoˈmorphic, ˌhomoeoˈmorphous adj ho•me•o•mor•phism (ˌhoʊ mi əˈmɔr fɪz əm) n. a mathematical function between two topological spaces that is continuous, one-to-one, and onto, and the inverse of which is continuous. [1850–55] ho`me•o•mor′phic, ho`me•o•mor′phous, adj. homeomorphism the similarity of the crystalline forms of substances that have different chemical compositions. — homeomorphous, adj.See also: Physics Translations Homeomorphism homeomorphism [¦hō·mē·ə¦mȯr‚fiz·əm] (mathematics) A continuous map between topological spaces which is one-to-one, onto, and its inverse function is continuous. Also known as bicontinuous function; topological mapping. Homeomorphism one of the basic concepts of topology. Two figures (more precisely, two topological spaces) are said to be homeomorphic if there exists a one-to-one continuous mapping of any one onto the other, for which the inverse mapping is also continuous. In this case, the mapping itself is called a homeomorphism. For example, any circle is homeomorphic to any square; any two segments are homeomorphic, but a segment is not homeomorphic to a circle or a line. A line is homeomorphic to any interval (that is, a segment without end points). The concept of homeomorphism is the basis for defining the extremely important concept of a topological property. Specifically, a property of a figure F is said to be topological if it is found in all figures homeomorphic to F. Examples of topological properties are compactness and connectedness. A. V. ARKHANGEL’SKII
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