| 释义 |
topology|təʊˈpɒlədʒɪ|
[f. topo- + -logy. Cf. F. topologique adj., Littré, related to sense 1 b.]
A term meaning ‘science of place’, which has been tentatively proposed or used in various senses.
1.
†a. The department of botany which treats of the localities where plants are found. Obs.
1659Lovell Compl. Herball Pref., The Topologie or place of gathering them. Thus, Herbes, are to be gathered in mountaines, hills and plain places.
†b. The art of assisting the memory by associating the thing to be remembered with some place or building, the parts of which are well known. Obs.
1860Worcester cites Fleming. Hence in later Dicts.
c. Anat.: see quot.
1899Syd. Soc. Lex., Topology, topographic anatomy. The relation of the presenting part of fœtus to the pelvic canal.
2. The scientific study of a particular locality: see quot. 19051.
1850S. Tymms Bury Wills (Camden) Introd. 12 The selection of wills..has been made more with a view to illustrate the peculiar customs and language of the period than the topology or genealogy of the district. 1902Cassell's Encycl. Dict. Suppl., Topology, the study of the places or localities in a given district. 1903Cornh. Mag. Feb. 251 The fact that topology is not synonymous with topography, but bears the same relation to topography as geology does to geography. 1905Q. Rev. Apr. 346 The comparatively new study of topology, the science by which, from the consideration of geographical facts about a locality, one can draw deductions as to its history. 1905Spectator 10 June 856/1 We need a knowledge not only of topography, but..of that..sister science which has been christened ‘topology’.
3. a. The branch of mathematics concerned with those properties of figures and surfaces which are independent of size and shape and are unchanged by any deformation that is continuous, neither creating new points nor fusing existing ones; hence, with those of abstract spaces that are invariant under homœomorphic transformations. [ad. G. topologie (J. B. Listing 1847, in Göttinger Studien i. 814).]
1883Nature 1 Feb. 316/2 The term Topology was introduced by Listing to distinguish what may be called qualitative geometry from the ordinary geometry in which quantitative relations chiefly are treated. 1895Funk's Standard Dict., Topology..2. Geom. The geometrical theory of situation without respect to size or shape, including the theory of knots in a closed curve and the relations of the bounding parts of a solid. 1929Trans. Amer. Math. Soc. XXXI. 290 Analysis situs or topology is primarily concerned with invariants under homeomorphic transformations of a space into itself. 1952F. Bagemihl et al. tr. Pontryagin's Found. Combinatorial Topol. i. 1 Combinatorial topology studies geometric forms by decomposing them into the simplest geometric figures, simplexes, which adjoin one another in a regular fashion. 1959E. M. Patterson Topology i. 1 Nowadays mathematicians are in fairly general agreement that topology is a study of continuity. 1970Observer (Colour Suppl.) 15 Feb. 19/2 Topology is one of the most recent and rapidly advancing branches of mathematics, and is a kind of universal geometry of surfaces. 1972M. Kline Math. Thought l. 1158 Topology, as it is understood in this century, breaks down into two somewhat separate divisions: point set topology, which is concerned with geometrical figures regarded as collections of points..; and combinatorial or algebraic topology, which treats geometrical figures as aggregates of smaller building blocks. 1975I. Stewart Concepts Mod. Math. x. 146 The basic objects studied in topology are called topological spaces.
b. (The study of) the topological properties of something. Also transf.
1913Amer. Jrnl. Math. XXXV. 189 An application..of the transformation by inversion to the topology of plane curves. 1930Proc. Nat. Acad. Sci. XVI. 240 (heading) Combinatory topology of convex regions. 1959Ibid. XLV. 1607 (heading) On the topology of the genetic fine structure. 1972Sci. Amer. Jan. 65/1 With careful dissection techniques one can expose deep-lying sections of bulk specimens so that their topology can be studied by scanning electron microscopy. 1980D. L. Cohn Measure Theory p. vii, Chapters 1 through 5..presuppose only the familiarity with the topology of Euclidean spaces that a student should acquire in an advanced calculus course.
c. A family of open subsets of an abstract space such that the union of any of the subsets and the intersection of any two of them are members of the family, together with the space itself and the null set.
1946E. Lehmer tr. Pontryagin's Topological Groups iii. 55 A topology can be introduced into any abstract group G whatsoever in such a way that G becomes a discrete group. 1963M. J. Mansfield Introd. Topol. ii. 21 The topologies {scrS} and {scrU} for R..were defined, in effect by specifying neighborhoods for each point and then declaring a set to be a member of the topology if and only if the set contains a neighborhood of each of its points. 1976Physics Bull. Sept. 388/2 A useful way to think of a topology for a space is as a specification of which functions on it are to be continuous.
d. gen. The way in which constituent parts are interrelated or arranged.
1967Electronics 6 Mar. 149/1 If consideration is restricted to bipolar gate topologies..there are just three basic forms of IC logic schemes. 1970Nature 7 Nov. 553/1 These data have been used to construct a topology based on the minimal mutation distance method... This topology places castor..closest to sesame.., then mung bean.., then sunflower. 1971Physics Bull. Dec. 717/3 Having an axisymmetric topology permits an easier study [of tokamaks] than, say, stellarators. 1972Computer Jrnl. XV. 204/1 The resulting list structure has the same topology as the old, so that re-entrancy and sharing of common substructure are preserved.
Hence toˈpologist, one versed in topology.
1903Cornh. Mag. Feb. 258 The French topologist has shown that the Odyssey is subsequent to a vanished Phœnician sea power. 1905Spectator 10 June 856/1 To the topographist..the site..is a mystery; to the topologist..it is full of meaning. 1954Sci. News XXXIII. 56 If you cross the curve..you must go from one part to another—you cannot stay inside or stay outside. I think that anyone who is not a topologist will accept this as a self-evident fact. 1967G. Steiner Lang. & Silence 33, I have watched topologists, knowing no syllable of each other's language, working effectively together at a blackboard. 1971I. G. Gass et al. Understanding Earth iv. 77/1 It is not what the topologists call a simply connected body; it is like a Henry Moore statue: it has a hole in it. 1975I. Stewart Concepts Mod. Math. x. 146 The oft-quoted assertion that to a topologist a doughnut is the same as a coffee-cup provides an example. |