On generalization of homotopy axiom

Author:

Karimov Umed

Abstract

In [S. Kermit, Proc. Amer. Math. Soc., 1972, 31(1):271-275] it was proven that if G is compact topological group or field then in the homotopy axiom for Alexander-Spanier-Kolmogoroff cohomology the parameter segment [0;1] can be replaced by any compact connected space T. The purpose of the paper is to show that the parameter space T can not be replaced in general by locally compact connected space.

Publisher

Odesa National University of Technology

Subject

Applied Mathematics,Geometry and Topology,Analysis

Reference9 articles.

1. [1] E. M. Beniaminov. Spectral sequence of a continuous mapping and of a covering for the Deheuvels homology. Mat. Sb. (N.S.), 88(130):211-217, 1972.

2. doi:10.1070/SM1972v017n02ABEH001499.

3. [2] Satya Deo. On the tautness property of Alexander-Spanier cohomology. Proc. Amer. Math. Soc., 52:441-444, 1975. doi:10.2307/2040179.

4. [3] Samuel Eilenberg and Norman Steenrod. Foundations of algebraic topology. Princeton University Press, Princeton, NJ, 1952.

5. [4] A. È. Harlap. Local homology and cohomology, homological dimension, and generalized manifolds. Mat. Sb. (N.S.), 96(138):347-373, 503, 1975.

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