homotopyn.
/ˈhɒməʊtɒpi//həˈmɒtəpi/ Mathematics.
a. A mapping that deforms one path continuously into another in such a way that all the intermediate paths lie within the topological space of which the two given paths are subspaces (see quot. 1970).
ΘΚΠ
the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > other
adjunction1891
homotopy1918
functor1942
1918 O. Veblen Analysis Situs (Cambridge Colloq. Lect., Vol. 5, Pt. 2) v. 126 The term homotopy will be used to designate a deformation in the general sense..and two generalized complexes..will be said to be homotopic if one can be carried into the other by means of a homotopy.
1930 S. Lefschetz Topol. ii. 77 The singular translation of A into A′ just described is called a homotopic deformation, or homotopy, or simply deformation.
1951 M. H. A. Newman Topol. Plane Sets of Points (ed. 2) vii. 179 It is homotopies..and not identities between paths that are interesting.
1970 C. R. F. Maunder Algebraic Topol. ii. 25 Two continuous maps f, g: X → Y are homotopic (or ‘f is homotopic to g’) if there exists a continuous map F: X × I → Y, such that F(x, 0) = f(x) and F(x, 1) = g(x), for all x ∈ X. The map F is said to be a homotopy, and we write f ≃ g for ‘f is homotopic to g’.
b. The property of being homotopic.
ΘΚΠ
the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > property of
invariance1878
invariancy1895
commutativity1929
commutativeness1949
homotopy1956
1956 E. M. Patterson Topol. i. 11 Homotopy plays an important part in modern topology.
1961 J. G. Hocking & G. S. Young Topol. iv. 151 Theorems about homotopy are but special cases of more general theorems on the extension of mappings.
This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2018).
<
n.1918