New constructions of topological invariants (of topological degree type), covering the majority of previously known ones, are introduced and investigated for a broad class of set-valued mappings. The topological structure of the set of fixed points of set-valued maps (including connectedness, topological dimension, acyclicity, etc.) is investigated. The topological dimension of the set of solutions of Cauchy problem for differential inclusions in finite-dimensional spaces is investigated. Solvability and topological dimension of the set of solutions of operator equations in the form $a(x)=f(x)$, where $ð$ is a surjective linear operator and $f$ is a copletely continuous operator, is investigated. For the infinite-dimensional Banach space a natural generalization of the classical Borsuk–Ulam finite-dimensional theorem is proved. A generalization of classical implicit function theorem is proved in the case where the Frechet derivative is a surjective operator.
Main publications:
Benkafadar N. M., Gel'man B. D. Generalized Local Degree for Multi-Valued Mappings // International Journal of Math., Game Theory and Algebra, 2000, 10(5), 413–434.
