| 释义 |
topoˈlogical, a.
[f. topology + -ical.]
1. Of or pertaining to topology (esp. in sense 2).
1715M. Davies Athen. Brit. I. 183 Another noted Historian..publish'd two *Topological Pamphlets, containing the Description of Britanny and Ireland. 1716Ibid. III. Diss. Physick 37 Ancient Chiron..the most direct Predecessor, at least in the topological Line, of the Great Hippocrates. 1836For. Q. Rev. XVII. 286 Except the following somewhat ingenious topological (not phrenological) explanation of Richter's genius. 1903Times 4 Apr. 7/2 The Azores..have a topological importance.
2. Math. 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 topological transformation = homœomorphism 2; topological space [tr. G. 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 3 c) on it.
1913Amer. Jrnl. Math. XXXV. 189 (heading) On some topological properties of plane curves and a theorem of Möbius. 1926Proc. Sect. Sci. K. Akad. van Wetenschappen te Amsterdam XXIX. 462 Any normal, not absolutely closed topological space {scrR} can be extended to a normal topological space R = {scrR} + ξ by adjunction of a non isolated point ξ. 1939M. 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. 1946E. Lehmer tr. Pontryagin's Topological 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[see homœomorphism 2]. 1961A. E. Farley tr. Alexandroff's Elem. Concepts Topology 16 A simple closed curve (i.e., the topological image of a circle). 1968E. T. Copson Metric Spaces vii. 92 Properties of a metric space which depend only on its open sets..are called topological properties. 1975I. Stewart Concepts Mod. Math. x. 144 Straightness is not a topological property.
Also topoˈlogic a.; topoˈlogically adv.
1716M. Davies Athen. Brit. III. Diss. Physick 12 They were distinguish'd topologically or Geographically. 1872M. Collins in Lett. & Friendships I. 113, I might go on with topologic lore, Until you voted me an awful bore. 1903Cornh. Mag. Feb. 259 The topologic compass keeps his prow true. 1915Trans. Amer. Math. Soc. XVI. 153 A manifold..topologically equivalent to the boundary of an n-dimensional complex. 1938Mind XLVII. 126 Tests are gauged ‘topologically’ by the extent to which they succeed in grouping together men who are also grouped together in respect of their performances in life. 1969R. B. Fuller Operating Man. Spaceship Earth v. 67 All the system's paths must be topologically and circularly interrelated. 1975I. Stewart Concepts Mod. Math. x. 156 Now topologically a dog is a sphere (assuming it keeps its mouth shut and neglecting internal organs) because all we have to do is shrink its legs and fatten it up a bit. |