topologyn.

/təʊˈpɒlədʒi/

Etymology: < topo- comb. form + -logy comb. form. Compare French topologique adjective, Littré, related to sense 1b.

A term meaning ‘science of place’, which has been tentatively proposed or used in various senses.

†a. The department of botany which treats of the localities where plants are found. Obsolete.

ΘΚΠ

the world > plants > botany > [noun] > specific branches or aspects of botany

phytognomy1643

topology1659

vegetable statics1691

cryptogamy1783

fossil botany1822

nomology1825

structural botany1835

phytochemistry1837

phytochimy1847

phytogeography1847

astrobotany1851

phytonomy1851

phytophysiology1854

palaeophytology1857

phytobiology1860

phytopathology1864

plant physiology1870

palaeobotany1872

plant geography1878

phytopalaeontology1879

plant pathology1891

ethnobotany1896

floristic1898

phyteconomy1898

phytoteratology1898

phytoecology1899

geobotany1904

phytosociology1917

archaeobotany1954

palaeoethnobotany1959

1659 R. Lovell Παμβοτανολογια 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. Obsolete.

ΚΠ

1860 J. E. Worcester Dict. Eng. Lang. (citing Fleming). Hence in later Dicts.

c. Anatomy: see quot. 1899.

ΘΚΠ

the world > life > the body > study of body > [noun] > human anatomy > regional

topography1847

topology1899

1899 New Sydenham Soc. Lexicon 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.

ΘΚΠ

the world > the earth > earth sciences > geography > [noun] > physical geography > topology or topography

topographyc1550

topographics1834

topology1850

1850 S. Tymms Wills & Inventories Bury St. Edmunds 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.

1903 Cornhill Mag. Feb. 251 The fact that topology is not synonymous with topography, but bears the same relation to topography as geology does to geography.

c1904 Encycl. Dict. Suppl. Topology, the study of the places or localities in a given district.

1905 Q. 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.

1905 Spectator 10 June 856/1 We need a knowledge not only of topography, but..of that..sister science which has been christened ‘topology’.

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. [ < German topologie (J. B. Listing 1847, in Göttinger Studien i. 814).]

ΘΚΠ

the world > relative properties > number > geometry > [noun] > branches of > topology

analysis situs1792

topology1883

1883 Nature 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.

1895 I. K. Funk et al. Standard Dict. Eng. Lang. II. 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.

1929 Trans. Amer. Math. Soc. 31 290 Analysis situs or topology is primarily concerned with invariants under homeomorphic transformations of a space into itself.

1952 F. Bagemihl et al. tr. L. S. Pontryagin Found. Combinatorial Topology i. 1 Combinatorial topology studies geometric forms by decomposing them into the simplest geometric figures, simplexes, which adjoin one another in a regular fashion.

1959 E. M. Patterson Topol. i. 1 Nowadays mathematicians are in fairly general agreement that topology is a study of continuity.

1970 Observer 15 Feb. (Colour Suppl.) 19/2 Topology is one of the most recent and rapidly advancing branches of mathematics, and is a kind of universal geometry of surfaces.

1972 M. 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.

1975 I. 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 transferred.

ΘΚΠ

the world > relative properties > number > geometry > [noun] > branches of > topology > study of

topology1913

1913 Amer. Jrnl. Math. 35 189 An application..of the transformation by inversion to the topology of plane curves.

1930 Proc. National Acad. Sci. U.S.A. 16 240 (heading) Combinatory topology of convex regions.

1959 Proc. National Acad. Sci. U.S.A. 45 1607 (heading) On the topology of the genetic fine structure.

1972 Sci. 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.

1980 D. 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.

ΘΚΠ

the world > relative properties > number > geometry > geometric space > [noun] > topological > division or part of

triangulation1940

topology1946

1946 E. Lehmer tr. L. S. Pontryagin Topol. Groups iii. 55 A topology can be introduced into any abstract group G whatsoever in such a way that G becomes a discrete group.

1963 M. J. Mansfield Introd. Topol. ii. 21 The topologies  and  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.

1976 Physics 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.

ΚΠ

1967 Electronics 6 Mar. 149/1 If consideration is restricted to bipolar gate topologies..there are just three basic forms of IC logic schemes.

1970 Nature 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.

1971 Physics Bull. Dec. 717/3 Having an axisymmetric topology permits an easier study [of tokamaks] than, say, stellarators.

1972 Computer Jrnl. 15 204/1 The resulting list structure has the same topology as the old, so that re-entrancy and sharing of common substructure are preserved.

Derivatives

toˈpologist n. one versed in topology.

ΘΚΠ

the world > the earth > earth sciences > geography > geographer > [noun] > physical geographer > topologist

topologist1903

the world > relative properties > number > geometry > [noun] > branches of > topology > one who studies

topologist1903

1903 Cornhill Mag. Feb. 258 The French topologist has shown that the Odyssey is subsequent to a vanished Phœnician sea power.

1905 Spectator 10 June 856/1 To the topographist..the site..is a mystery; to the topologist..it is full of meaning.

1954 Sci. News 33 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.

1967 G. Steiner Lang. & Silence 33 I have watched topologists, knowing no syllable of each other's language, working effectively together at a blackboard.

1971 I. 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.

1975 I. 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.

This entry has not yet been fully updated (first published 1913; most recently modified version published online September 2021).

单词	topology
释义	topologyn. /təʊˈpɒlədʒi/ Etymology: < topo- comb. form + -logy comb. form. Compare French topologique adjective, Littré, related to sense 1b. 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. Obsolete. ΘΚΠ the world > plants > botany > [noun] > specific branches or aspects of botany phytognomy1643 topology1659 vegetable statics1691 cryptogamy1783 fossil botany1822 nomology1825 structural botany1835 phytochemistry1837 phytochimy1847 phytogeography1847 astrobotany1851 phytonomy1851 phytophysiology1854 palaeophytology1857 phytobiology1860 phytopathology1864 plant physiology1870 palaeobotany1872 plant geography1878 phytopalaeontology1879 plant pathology1891 ethnobotany1896 floristic1898 phyteconomy1898 phytoteratology1898 phytoecology1899 geobotany1904 phytosociology1917 archaeobotany1954 palaeoethnobotany1959 1659 R. Lovell Παμβοτανολογια 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. Obsolete. ΚΠ 1860 J. E. Worcester Dict. Eng. Lang. (citing Fleming). Hence in later Dicts. c. Anatomy: see quot. 1899. ΘΚΠ the world > life > the body > study of body > [noun] > human anatomy > regional topography1847 topology1899 1899 New Sydenham Soc. Lexicon 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. ΘΚΠ the world > the earth > earth sciences > geography > [noun] > physical geography > topology or topography topographyc1550 topographics1834 topology1850 1850 S. Tymms Wills & Inventories Bury St. Edmunds 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. 1903 Cornhill Mag. Feb. 251 The fact that topology is not synonymous with topography, but bears the same relation to topography as geology does to geography. c1904 Encycl. Dict. Suppl. Topology, the study of the places or localities in a given district. 1905 Q. 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. 1905 Spectator 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. [ < German topologie (J. B. Listing 1847, in Göttinger Studien i. 814).] ΘΚΠ the world > relative properties > number > geometry > [noun] > branches of > topology analysis situs1792 topology1883 1883 Nature 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. 1895 I. K. Funk et al. Standard Dict. Eng. Lang. II. 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. 1929 Trans. Amer. Math. Soc. 31 290 Analysis situs or topology is primarily concerned with invariants under homeomorphic transformations of a space into itself. 1952 F. Bagemihl et al. tr. L. S. Pontryagin Found. Combinatorial Topology i. 1 Combinatorial topology studies geometric forms by decomposing them into the simplest geometric figures, simplexes, which adjoin one another in a regular fashion. 1959 E. M. Patterson Topol. i. 1 Nowadays mathematicians are in fairly general agreement that topology is a study of continuity. 1970 Observer 15 Feb. (Colour Suppl.) 19/2 Topology is one of the most recent and rapidly advancing branches of mathematics, and is a kind of universal geometry of surfaces. 1972 M. 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. 1975 I. 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 transferred. ΘΚΠ the world > relative properties > number > geometry > [noun] > branches of > topology > study of topology1913 1913 Amer. Jrnl. Math. 35 189 An application..of the transformation by inversion to the topology of plane curves. 1930 Proc. National Acad. Sci. U.S.A. 16 240 (heading) Combinatory topology of convex regions. 1959 Proc. National Acad. Sci. U.S.A. 45 1607 (heading) On the topology of the genetic fine structure. 1972 Sci. 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. 1980 D. 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. ΘΚΠ the world > relative properties > number > geometry > geometric space > [noun] > topological > division or part of triangulation1940 topology1946 1946 E. Lehmer tr. L. S. Pontryagin Topol. Groups iii. 55 A topology can be introduced into any abstract group G whatsoever in such a way that G becomes a discrete group. 1963 M. J. Mansfield Introd. Topol. ii. 21 The topologies  and  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. 1976 Physics 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. ΚΠ 1967 Electronics 6 Mar. 149/1 If consideration is restricted to bipolar gate topologies..there are just three basic forms of IC logic schemes. 1970 Nature 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. 1971 Physics Bull. Dec. 717/3 Having an axisymmetric topology permits an easier study [of tokamaks] than, say, stellarators. 1972 Computer Jrnl. 15 204/1 The resulting list structure has the same topology as the old, so that re-entrancy and sharing of common substructure are preserved. Derivatives toˈpologist n. one versed in topology. ΘΚΠ the world > the earth > earth sciences > geography > geographer > [noun] > physical geographer > topologist topologist1903 the world > relative properties > number > geometry > [noun] > branches of > topology > one who studies topologist1903 1903 Cornhill Mag. Feb. 258 The French topologist has shown that the Odyssey is subsequent to a vanished Phœnician sea power. 1905 Spectator 10 June 856/1 To the topographist..the site..is a mystery; to the topologist..it is full of meaning. 1954 Sci. News 33 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. 1967 G. Steiner Lang. & Silence 33 I have watched topologists, knowing no syllable of each other's language, working effectively together at a blackboard. 1971 I. 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. 1975 I. 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. This entry has not yet been fully updated (first published 1913; most recently modified version published online September 2021). < n.1659
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