Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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The generalized homotopy axiom and its consistency with Alexandroff-Čech cohomology theory.

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Published Nov 6, 2025
DOI https://doi.org/10.15673/pigc.v18i3.3068

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Umed Karimov
Institute of Mathematics Tajik Academy of Sciences

Abstract

Let T be a connected compact metric space, r,s ∈ T be two points, and X be a locally compact paracompact space. We prove that the mappings φr, φs: X → X × T, defined by φt(x) = (x,t) for t=r, s ∈ T, induce the same homomorphisms of Alexandroff-Čech cohomology if and only if the following natural homomorphism π:Ȟ(T,{r,s}) → Ȟ(T) splits.

Keywords:
Alexandroff-Čech cohomology, Sheaf cohomology, inverse limit, exact sequence, homotopy axiom, nerve of covering

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How to Cite
Karimov, U. (2025). The generalized homotopy axiom and its consistency with Alexandroff-Čech cohomology theory. Proceedings of the International Geometry Center, 18(3), 249-261. https://doi.org/10.15673/pigc.v18i3.3068
Issue
Vol 18 No 3 (2025)
Section
Papers
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