Self-closeness number and weak homotopy decomposition.

2021 ◽  
Author(s):  
Ho Won Choi ◽  
Kee Young Lee
Keyword(s):  
Homotopy Decomposition ◽  
Weak Homotopy

scholarly journals Spaces which Invert Weak Homotopy Equivalences

2018 ◽  
Vol 62 (2) ◽  
pp. 553-558
Author(s):  
Jonathan Ariel Barmak
Keyword(s):  
Empty Space ◽  
Weak Equivalence ◽  
Homotopy Equivalence ◽  
Homotopy Classes ◽  
Cw Complex ◽  
Cw Complexes ◽  
Weak Homotopy ◽  
Weak Homotopy Equivalence

AbstractIt is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f* : [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f* : [B, X] → [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible.

A Counterexample to a Conjecture of D. B. Fuks

1970 ◽  
Vol 13 (2) ◽  
pp. 261-266
Author(s):  
Luc Demers
Keyword(s):  
Homotopy Types ◽  
Weak Homotopy

In [3] D. B. Fuks defined a duality of functors in the category of weak homotopy types. In general this duality is more difficult to work with than the duality of functors of the category of pointed Kelley spaces [2]. It happens however that all so-called strong functors [2] F of induce functors of , and if we denote the duality operators of and by and D respectively, then there are many cases where .

scholarly journals Cohomology of Homotopy Colimits of Simplicial Sets and Small Categories

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 981
Author(s):  
Antonio M. Cegarra
Keyword(s):  
Simplicial Sets ◽  
Local Coefficients ◽  
Weak Homotopy

This paper deals with well-known weak homotopy equivalences that relate homotopy colimits of small categories and simplicial sets. We show that these weak homotopy equivalences have stronger cohomology-preserving properties than for local coefficients.

Homotopy Decompositions Involving the Loops of Coassociative Co-H Spaces

2003 ◽  
Vol 55 (1) ◽  
pp. 181-203 ◽  
Author(s):  
Stephen D. Theriault
Keyword(s):  
Homotopy Decomposition

AbstractJames gave an integral homotopy decomposition of ∑Ω∑X, Hilton-Milnor one for Ω(∑X ∨ ∑Y), and Cohen-Wu gave p-local decompositions of Ω∑X if X is a suspension. All are natural. Using idempotents and telescopes we show that the James andHilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-H spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-H space.

scholarly journals Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Abdon Atangana ◽  
Adem Kılıçman
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Biharmonic Equations ◽  
Poisson Equations ◽  
Physical Problems ◽  
Adomian Decomposition ◽  
Homotopy Decomposition ◽  
2D And 3D ◽  
Corrected Function

The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as tends to infinity.

scholarly journals Homotopy decomposition of a suspended real toric space

2016 ◽  
Vol 23 (1) ◽  
pp. 153-161 ◽  
Author(s):  
Suyoung Choi ◽  
Shizuo Kaji ◽  
Stephen Theriault
Keyword(s):  
Homotopy Decomposition
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