MAPPINGS WITH UNCOUNTABLY MANY TOPOLOGICALLY CRITICAL POINTS AND APPLICATIONS TO SOME CURVATURE PROBLEMS

Abstract

In this paper we improve the results of [9, 10] showing that, under certain topological conditions, the topological phi-category of a pair (M, N) of topological manifolds is infinite uncountable. The improved result is then applied to improve the results of [4], showing that various Ltop categories are infinite uncountable.