Noncompact absolute extensors in dimension $n$, $n$-soft mappings, and their applications

$R$-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.