| 释义 |
homotopy Math.|ˈhɒməʊtɒpɪ, həˈmɒtəpɪ|
[ad. G. homotopie (Dehn & Heegaard Analysis Situs in Encykl. d. math. Wiss. (1907) III. i. i. 164): see prec. and -y3.]
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).
b. The property of being homotopic.
1918O. 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. 1930S. Lefschetz Topology ii. 77 The singular translation of A into A′ just described is called a homotopic deformation, or homotopy, or simply deformation. 1951M. H. A. Newman Topology of Plane Sets of Points (ed. 2) vii. 179 It is homotopies..and not identities between paths that are interesting. 1956E. M. Patterson Topology i. 11 Homotopy plays an important part in modern topology. 1961Hocking & Young Topology iv. 151 Theorems about homotopy are but special cases of more general theorems on the extension of mappings. 1970C. R. F. Maunder Algebraic Topology 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 {elem} X. The map F is said to be a homotopy, and we write f ≃ g for ‘f is homotopic to g’. |