homoeomorphismn.

/hɒmiːəʊˈmɔːfɪz(ə)m/

Forms: Also homeomorphism.

Etymology: < homoeo- comb. form + -morphism comb. form.

1. Crystallography. Homoeomorphous constitution.

ΚΠ

1854 Dana in Amer. Jrnl. Sc. 18 35 (title) On the Homœomorphism of the Mineral Species of the Trimetric System.

1865–72 H. Watts Dict. Chem. III. 432 An interesting example of homœomorphism is afforded by nitrate of potassium, which is dimorphous, having a rhombohedral form similar to that of calcspar, and a trimetric form like that of arragonite.

2. Usually homeo-. Mathematics. [ < French homéomorphisme (H. Poincaré 1895, in Jrnl. de l'École polytechn. I. 7).] A one-to-one transformation of one complex or topological space on to another that is continuous and has a continuous inverse; a topological transformation; a topological equivalence between two figures.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements

inclusion1870

orthomorphosis1885

isomorphism1892

identity1910

homoeomorphism1918

homomorphism1935

topological mapping or transformation1939

isometry1941

Möbius transformation1941

injection map(ping)1950

monomorphism1954

bijection1963

surjection1964

1918 O. Veblen Analysis Situs (Cambridge Colloq. Lect., Vol. 5, Pt. 2) i. 3 A (1–1) continuous transformation of a complex into itself or another complex is called, following Poincaré, a homeomorphism.

1929 Fundamenta Math. XIV. 94 Let I₁ be the interval from (0, 1) to (0, 0) in a plane E₂, and let Φ be a homeomorphism between the arc x₁y₁ and the interval I₁.

1956 E. M. Patterson Topol. i. 2 The fundamental type of equivalence in topology is called topological equivalence or homeomorphism.

1961 S. S. Cairns Introd. Topol. iii. 54 Topology is the study of those properties of spaces which are preserved by homeomorphisms.

1965 S. Barr Exper. Topol. vi. 77 There is one crossing of the edge with itself at C, which cannot be removed by distortion, or even the cutting and re-joining allowed by homoeomorphism.

1969 A. T. Lundell & S. Weingram Topol. CW Complexes ii. 46 Since each cell σ of X is compact and Y is Hausdorff, f|σ is a homeomorphism onto its image cell τ ⊂ Y.

This entry has not yet been fully updated (first published 1976; most recently modified version published online December 2020).

单词	homoeomorphism
释义	homoeomorphismn. /hɒmiːəʊˈmɔːfɪz(ə)m/ Forms: Also homeomorphism. Etymology: < homoeo- comb. form + -morphism comb. form. 1. Crystallography. Homoeomorphous constitution. ΚΠ 1854 Dana in Amer. Jrnl. Sc. 18 35 (title) On the Homœomorphism of the Mineral Species of the Trimetric System. 1865–72 H. Watts Dict. Chem. III. 432 An interesting example of homœomorphism is afforded by nitrate of potassium, which is dimorphous, having a rhombohedral form similar to that of calcspar, and a trimetric form like that of arragonite. 2. Usually homeo-. Mathematics. [ < French homéomorphisme (H. Poincaré 1895, in Jrnl. de l'École polytechn. I. 7).] A one-to-one transformation of one complex or topological space on to another that is continuous and has a continuous inverse; a topological transformation; a topological equivalence between two figures. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements inclusion1870 orthomorphosis1885 isomorphism1892 identity1910 homoeomorphism1918 homomorphism1935 topological mapping or transformation1939 isometry1941 Möbius transformation1941 injection map(ping)1950 monomorphism1954 bijection1963 surjection1964 1918 O. Veblen Analysis Situs (Cambridge Colloq. Lect., Vol. 5, Pt. 2) i. 3 A (1–1) continuous transformation of a complex into itself or another complex is called, following Poincaré, a homeomorphism. 1929 Fundamenta Math. XIV. 94 Let I₁ be the interval from (0, 1) to (0, 0) in a plane E₂, and let Φ be a homeomorphism between the arc x₁y₁ and the interval I₁. 1956 E. M. Patterson Topol. i. 2 The fundamental type of equivalence in topology is called topological equivalence or homeomorphism. 1961 S. S. Cairns Introd. Topol. iii. 54 Topology is the study of those properties of spaces which are preserved by homeomorphisms. 1965 S. Barr Exper. Topol. vi. 77 There is one crossing of the edge with itself at C, which cannot be removed by distortion, or even the cutting and re-joining allowed by homoeomorphism. 1969 A. T. Lundell & S. Weingram Topol. CW Complexes ii. 46 Since each cell σ of X is compact and Y is Hausdorff, f\|σ is a homeomorphism onto its image cell τ ⊂ Y. This entry has not yet been fully updated (first published 1976; most recently modified version published online December 2020). < n.1854
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