On generalization of homotopy axiom

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.