Retractions in homotopy theory for finite topological semigroups

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Amin Saif ◽  
Hakeem A. Othman
Keyword(s):  
Homotopy Theory ◽  
Topological Semigroups

Tx -Fibrations in Homotopy Theory for Topological Semigroups

2016 ◽  
Vol 3 (2) ◽  
pp. 47-55
Author(s):  
Amin Saif ◽  
Adem Kılıcman
Keyword(s):  
Homotopy Theory ◽  
Topological Semigroups

scholarly journals Homotopy Extension Property in Homotopy Theory for Topological Semigroups

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Adem Kılıçman ◽  
Amin Saif
Keyword(s):  
Homotopy Theory ◽  
Extension Property ◽  
Topological Spaces ◽  
Topological Semigroups

The purpose of this paper is to extend the concept of homotopy extension property in homotopy theory for topological spaces to its analogical structure in homotopy theory for topological semigroups. In this extension, we also give some results concerning on absolutely retract and its properties.

On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups

2003 ◽  
Vol 10 (2) ◽  
pp. 209-222
Author(s):  
I. Bakhia
Keyword(s):  
Wide Class ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Topological Groups ◽  
Compact Spaces ◽  
Topological Semigroups

Abstract Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

Topological Left Amenability of Semidirect Products

1981 ◽  
Vol 24 (1) ◽  
pp. 79-85 ◽  
Author(s):  
H. D. Junghenn
Keyword(s):  
Large Class ◽  
Semidirect Product ◽  
Locally Compact ◽  
Semidirect Products ◽  
Topological Semigroups

AbstractLet S and T be locally compact topological semigroups and a semidirect product. Conditions are determined under which topological left amenability of S and T implies that of , and conversely. The results are used to show that for a large class of semigroups which are neither compact nor groups, various notions of topological left amenability coincide.

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