| 释义 |
homœomorphism|hɒmiːəʊˈmɔːfɪz(ə)m|
Also homeo-.
[f. homœo- + Gr. µορϕ-ή shape + -ism.]
1. Cryst. Homœomorphous constitution.
1854Dana in Amer. Jrnl. Sc. XVIII. 35 (title) On the Homœomorphism of the Mineral Species of the Trimetric System. 1865–72Watts 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. (Usu. homeo-.) Math. [ad. F. 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.
1918O. 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. 1929Fundamenta 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. 1956E. M. Patterson Topology i. 2 The fundamental type of equivalence in topology is called topological equivalence or homeomorphism. 1961S. S. Cairns Introd. Topology iii. 54 Topology is the study of those properties of spaces which are preserved by homeomorphisms. 1965S. Barr Exper. Topology 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. 1969Lundell & Weingram Topology CW Complexes ii. 46 Since each cell σ of X is compact and Y is Hausdorff, f{vb}σ is a homeomorphism onto its image cell τ ⊂ Y. |