topologicaladj.
1. Of or pertaining to topology (esp. in sense 2).
ΘΚΠ
the world > the earth > earth sciences > geography > [adjective] > physical geography > topology or topography
topographicala1586
topographic1632
topological1715
topologic1872
topo1970
1715 M. Davies Εἰκων Μικρο-βιβλικὴ 183 Another noted Historian..publish'd two Topological Pamphlets, containing the Description of Britanny and Ireland.
1716 Athenæ Britannicæ III. Diss. Physick 37 Ancient Chiron..the most direct Predecessor, at least in the topological Line, of the Great Hippocrates.
1836 Foreign Q. Rev. 17 286 Except the following somewhat ingenious topological (not phrenological) explanation of Richter's genius.
1903 Times 4 Apr. 7/2 The Azores..have a topological importance.
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.
Derivatives
topoˈlogic adj.
ΘΚΠ
the world > the earth > earth sciences > geography > [adjective] > physical geography > topology or topography
topographicala1586
topographic1632
topological1715
topologic1872
topo1970
1872 M. Collins in Lett. & Friendships I. 113 I might go on with topologic lore, Until you voted me an awful bore.
1903 Cornhill Mag. Feb. 259 The topologic compass keeps his prow true.
topoˈlogically adv.
ΘΚΠ
the world > the earth > earth sciences > geography > [adverb] > physical geography > topology or topography
topographically1625
topologically1716
the world > relative properties > number > geometry > [adverb]
geometrically1555
trigonometrically1666
topologically1915
stereometrically1928
1716 M. Davies Diss. Physick 12 in Athenæ Britannicæ III They were distinguish'd topologically or Geographically.
1915 Trans. Amer. Math. Soc. 16 153 A manifold..topologically equivalent to the boundary of an n-dimensional complex.
1938 Mind 47 126 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.
1969 R. B. Fuller Operating Man. Spaceship Earth v. 67 All the system's paths must be topologically and circularly interrelated.
1975 I. 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.
This entry has not yet been fully updated (first published 1986; most recently modified version published online June 2019).
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adj.1715