| 释义 |
homœomorphic, a.|hɒmiːəʊˈmɔːfɪk|
Also homeo-.
[f. as next + -ic.]
1. gen. Of the same kind or form.
1902Buck's Handbk. Med. Sci. (rev. ed.) IV. 660/1 In a remarkable proportion of cases of mental and other nervous disturbances we find a history of antecedent nervous conditions, either homoeomorphic, i.e. of the same order, or heteromorphic, of different type.
b. Palæont. = homœomorphous a. c.
1923H. H. Swinnerton Outl. Palæont. x. 214 These forms presented homeomorphic resemblances to Amaltheus.
2. (Usu. homeo-.) Math. [ad. F. homéomorphe (H. Poincaré 1895, in Jrnl. de l'École polytechn. I. 9).] Related by a homœomorphism, topologically equivalent to a complex, figure, or topological space; that is a homœomorphism.
1918O. Veblen Analysis Situs (Cambridge Colloq. Lect., Vol. 5, Pt. 2) i. 3 Two complexes related by a homeomorphism are said to be homeomorphic. 1926Trans. Amer. Math. Soc. XXVIII. 4 The manifold condition is equivalent to demanding that all these complexes be homeomorphic to cell boundaries. 1932Ann. Math. XXXIII. 550 The isomorphism..induces a homeomorphic (i.e., a one–one bi-continuous) correspondence between the points of the two group spaces. 1956E. M. Patterson Topology i. 6 Topologically, the Möbius band is a different surface from the cylinder, which means that the two surfaces are not homeomorphic. 1967F. Harary Seminar on Graph Theory ii. 15 A subdivision of a graph G is any graph obtainable from G by replacing some line uv of G by a new point w and two new lines uw and wv. Two graphs are homeomorphic if there is a third graph which can be obtained from each by a sequence of subdivisions. 1967D. W. Blackett Elem. Topology i. 13 Any two circles are homeomorphic and..any circle is homeomorphic to any square. On the other hand, a circle and a figure eight are not homeomorphic.
Hence homœoˈmorphically adv. Math., in a way that preserves all topological properties.
1927Trans. Amer. Math. Soc. XXIX. 438 Two h-cells can be homeomorphically transformed into one another in such manner that two (h—1)-cells of their boundaries are similarly transformed. 1965S. Barr Exper. Topology i. 6 If we draw a triangle on a lump of Plasticine, it is conceivably possible to distort it homoeomorphically so as to get rid of the three angles and make it into a circle. |