On the Deformation Retraction of Some Function Spaces Associated With the Relative Homotopy Groups

1943 ◽  
Vol 44 (1) ◽  
pp. 51
Author(s):  
Ralph H. Fox
Keyword(s):  
Function Spaces ◽  
Homotopy Groups ◽  
Deformation Retraction

Gottlieb Sets and Duality in Homotopy Theory

1975 ◽  
Vol 27 (5) ◽  
pp. 1042-1055 ◽  
Author(s):  
I. G. Halbhavi ◽  
K. Varadarajan
Keyword(s):  
Homotopy Theory ◽  
Base Point ◽  
Function Spaces ◽  
Extensive Study ◽  
Homotopy Groups ◽  
Locally Compact ◽  
Homotopy Classes ◽  
Set Up

Evaluation subgroups of the homotopy groups have been objects of extensive study recently by Gottlieb, Haslam, Jerrold Siegel, G. E. Lang (Jr), etc. In [8] one of the authors has introduced the notions of ‘cyclic' and ‘cocyclic’ maps and studied generalizations of evaluation subgroups and their duals in the set up of Eckmann-Hilton duality. This paper continues the study of these generalized Gottlieb and dual Gottlieb subsets. All the spaces, except the function spaces, will be arc connected locally compact CW-complexes with base point at a vertex. For any X, Y the set of base point preserving homotopy classes of maps of X to Y is denoted by [X, Y].

On Homotopy Groups of Function Spaces

1952 ◽  
Vol 74 (1) ◽  
pp. 241 ◽  
Author(s):  
James R. Jackson
Keyword(s):  
Function Spaces ◽  
Homotopy Groups

scholarly journals Gottlieb groups of function spaces

2015 ◽  
Vol 159 (1) ◽  
pp. 61-77 ◽  
Author(s):  
GREGORY LUPTON ◽  
SAMUEL BRUCE SMITH
Keyword(s):  
Finite Groups ◽  
Loop Space ◽  
Betti Numbers ◽  
Function Spaces ◽  
Homotopy Groups ◽  
Free Loop Space ◽  
Simply Connected

AbstractWe analyse the Gottlieb groups of function spaces. Our results lead to explicit decompositions of the Gottlieb groups of many function spaces map(X, Y)—including the (iterated) free loop space of Y—directly in terms of the Gottlieb groups of Y. More generally, we give explicit decompositions of the generalised Gottlieb groups of map(X, Y) directly in terms of generalised Gottlieb groups of Y. Particular cases of our results relate to the torus homotopy groups of Fox. We draw some consequences for the classification of T-spaces and G-spaces. For X, Y finite and Y simply connected, we give a formula for the ranks of the Gottlieb groups of map(X, Y) in terms of the Betti numbers of X and the ranks of the Gottlieb groups of Y. Under these hypotheses, the Gottlieb groups of map(X, Y) are finite groups in all but finitely many degrees.

scholarly journals On homotopy groups of function spaces

1955 ◽  
Vol 31 (4) ◽  
pp. 222-227
Author(s):  
Yoshiro Inoue
Keyword(s):  
Function Spaces ◽  
Homotopy Groups

Function Spaces and Nonsymmetric Norm Preserving Maps

2018 ◽  
Vol 25 (5) ◽  
pp. 729-740
Author(s):  
Hadis Pazandeh ◽  
Fereshteh Sady
Keyword(s):  
Function Spaces

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces
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