| 释义 |
homotopic, a.|hɒməʊˈtɒpɪk|
[f. homo- + Gr. τοπικ-ός in respect to place (see topic a. and n.).]
1. Relating to the same place or part, or corresponding places or parts.
1876tr. Haeckel's Hist. Creat. I. 217 The laws of homotopic transmission..which might be called the law of transmission in corresponding parts of the body.
2. Math. [ad. G. homotop (Dehn & Heegaard Analysis Situs in Encykl. d. math. Wiss. (1907) III. i. i. 165).] Related by a homotopy to another complex or path, or the mapping of which it is an image; that is a homotopy.
1918,1930[see homotopy]. 1956E. M. Patterson Topology i. 11 A curve which can be deformed continuously into another is said to be homotopic to it. 1961Hocking & Young Topology iv. 149 We may view homotopic mappings as being members of a one-parameter family of mappings with a continuous parameter. 1967W. S. Massey Algebraic Topology ii. 64 Two continuous maps ϕ0, ϕ1: X → Y are homotopic if and only if there exists a continuous map ϕ: X × I → Y such that, for x {elem} X, ϕ(x, 0) = ϕ0(x), ϕ(x, 1) = ϕ1(x).
Hence homoˈtopically adv., by a homotopy; as regards homotopy.
1930S. Lefschetz Topology ii. 77 We will say that A and A′ are homotopically deformable, or simply deformable, into one another, over G. 1952F. Bagemihl et al. tr. Pontryagin's Found. Combinatorial Topology iii. 83 The mappings ϕ and θ are said to be homotopically inverse to one another. 1968H. F. Cullen Introd. Gen. Topology vii. 368 The usual space E1 of real numbers is homotopically equivalent to the trivial space consisting of 0 alone, say. |
