NONCOMPACT ABSOLUTE EXTENSORS IN DIMENSION<i>n</i>,<i>n</i>-SOFT MAPPINGS, AND THEIR APPLICATIONS

Abstract

R-compact absolute extensors in dimension n (AE(n)) and n-soft mappings are defined and studied. Spectral characterizations are obtained not only for AE(n)-spaces but also for n-soft mappings themselves; this is new even in the compact case. The technique developed is applied to the study of certain questions of functional analysis and the theory of nonmetrizable manifolds modeled on topological vector spaces. Bibliography: 27 titles.