| 单词 | topological invariant |
| 释义 | > as lemmastopological invariant 2. Mathematics. Of or pertaining to topology; such as is dealt with by topology (sense 3); topological invariant, something invariant under a topological mapping; topological mapping or transformation = homoeomorphism n. 2; topological space [translating German topologisch raum (F. Hausdorff Grundzüge der Mengenlehre (1914) vii. 213); the sense is due to M. Fréchet ( Compt. Rend. (1925) CLXXX. 421)] , an abstract space together with a topology (sense 3c) on it. ΘΚΠ the world > relative properties > number > geometry > [adjective] > branches of stereometrical1656 Apollonian1704 Euclidean1714 isoperimetrical1743 stereotomical1828 stereotomic1860 stereometric1862 graphic1865 parabolic1872 metageometrical1882 pangeometrical1882 Riemannian1889 synthetic1889 polygonometric1890 Lobachevskian1896 topological1913 the world > relative properties > number > geometry > geometric space > [noun] > topological manifoldness1873 manifold1878 submanifold1898 function space1912 topological space1913 sheaf1955 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 1913 Amer. Jrnl. Math. 35 189 (heading) On some topological properties of plane curves and a theorem of Möbius. 1926 Proc. Sect. Sci. K. Akad. van Wetenschappen te Amsterdam XXIX. 462 Any normal, not absolutely closed topological space ℛ can be extended to a normal topological space R = ℛ + ξ by adjunction of a non isolated point ξ. 1939 M. H. A. Newman Elem. Topol. Plane Sets of Points iii. 51 The correlation is called a homoeomorphism between the spaces, or a topological mapping of the one space on the other. 1946 E. Lehmer tr. L. S. Pontryagin Topol. Groups iii. 53 For any two elements p and q of the group G there exists a topological transformation f(x) of the space G into itself which transforms p into q. 1956 E. M. Patterson Topol. i. 2 The fundamental type of equivalence in topology is called topological equivalence or homeomorphism. 1961 A. E. Farley tr. Alexandroff Elem. Concepts Topol. 16 A simple closed curve (i.e., the topological image of a circle). 1968 E. T. Copson Metric Spaces vii. 92 Properties of a metric space which depend only on its open sets..are called topological properties. 1975 I. Stewart Concepts Mod. Math. x. 144 Straightness is not a topological property. < as lemmas |
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