homotopicadj.

/hɒməʊˈtɒpɪk/

Etymology: < homo- comb. form + Greek τοπικός in respect to place (see topic adj. and n.).

1. Relating to the same place or part, or corresponding places or parts.

ΘΚΠ

the world > life > biology > physical aspects or shapes > specific areas or structures > [adjective] > same place or part

homotopic1876

1876 E. R. Lankester tr. E. Haeckel Hist. Creation I. 217 The laws of homotopic transmission..which might be called the law of transmission in corresponding parts of the body.

2. Mathematics. [ < German 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.

ΘΚΠ

the world > relative properties > number > geometry > [adjective] > of geometrical relation

reciprocal1570

regular1570

projectivea1652

semi-conjugate axis1743

homographic1859

symmetric1860

confocal1867

correlative1881

involutorial1885

conjugate1902

antisymmetrical1913

homoeomorphic1918

homotopic1918

isometric1952

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.

1956 E. M. Patterson Topol. i. 11 A curve which can be deformed continuously into another is said to be homotopic to it.

1961 J. G. Hocking & G. S. Young Topol. iv. 149 We may view homotopic mappings as being members of a one-parameter family of mappings with a continuous parameter.

1967 W. S. Massey Algebraic Topol. 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 ∈ X, ϕ(x, 0) = ϕ₀(x), ϕ(x, 1) = ϕ₁(x).

Derivatives

homoˈtopically adv. by a homotopy; as regards homotopy.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adverb]

alternately1570

homographically1859

birationally1915

homoeomorphically1927

homotopically1930

isomorphically1935

homomorphically1941

isometrically1959

symplectically1959

1930 S. Lefschetz Topol. ii. 77 We will say that A and A′ are homotopically deformable, or simply deformable, into one another, over G.

1952 F. Bagemihl et al. tr. L. S. Pontryagin Found. Combinatorial Topology iii. 83 The mappings ϕ and θ are said to be homotopically inverse to one another.

1968 H. F. Cullen Introd. Gen. Topol. vii. 368 The usual space E¹ of real numbers is homotopically equivalent to the trivial space consisting of 0 alone, say.

This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2019).

单词	homotopic
释义	homotopicadj. /hɒməʊˈtɒpɪk/ Etymology: < homo- comb. form + Greek τοπικός in respect to place (see topic adj. and n.). 1. Relating to the same place or part, or corresponding places or parts. ΘΚΠ the world > life > biology > physical aspects or shapes > specific areas or structures > [adjective] > same place or part homotopic1876 1876 E. R. Lankester tr. E. Haeckel Hist. Creation I. 217 The laws of homotopic transmission..which might be called the law of transmission in corresponding parts of the body. 2. Mathematics. [ < German 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. ΘΚΠ the world > relative properties > number > geometry > [adjective] > of geometrical relation reciprocal1570 regular1570 projectivea1652 semi-conjugate axis1743 homographic1859 symmetric1860 confocal1867 correlative1881 involutorial1885 conjugate1902 antisymmetrical1913 homoeomorphic1918 homotopic1918 isometric1952 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. 1956 E. M. Patterson Topol. i. 11 A curve which can be deformed continuously into another is said to be homotopic to it. 1961 J. G. Hocking & G. S. Young Topol. iv. 149 We may view homotopic mappings as being members of a one-parameter family of mappings with a continuous parameter. 1967 W. S. Massey Algebraic Topol. 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 ∈ X, ϕ(x, 0) = ϕ₀(x), ϕ(x, 1) = ϕ₁(x). Derivatives homoˈtopically adv. by a homotopy; as regards homotopy. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adverb] alternately1570 homographically1859 birationally1915 homoeomorphically1927 homotopically1930 isomorphically1935 homomorphically1941 isometrically1959 symplectically1959 1930 S. Lefschetz Topol. ii. 77 We will say that A and A′ are homotopically deformable, or simply deformable, into one another, over G. 1952 F. Bagemihl et al. tr. L. S. Pontryagin Found. Combinatorial Topology iii. 83 The mappings ϕ and θ are said to be homotopically inverse to one another. 1968 H. F. Cullen Introd. Gen. Topol. vii. 368 The usual space E¹ of real numbers is homotopically equivalent to the trivial space consisting of 0 alone, say. This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2019). < adj.1876
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