On a criterion of properness of multimaps

Details On a criterion of properness of multimaps On a criterion of properness of multimaps

2009-11-09

arxiv.org/abs/0911.1702v1

D.A. Vorotnikov. On a criterion of properness of multimaps, Trudy Molodykh Uchenykh Mat. Fak. VSU, 2003, pp. 23-27 (in Russian

Mathematics

Functional Analysis

3 pages, in Russian

Scientific paper

The close relation between properness and closedness of maps is well-known. For instance, for Fredholm mappings of infinite dimensional Banach manifolds, these properties are equivalent. On the other hand, properness of maps plays an important role for construction of various topological degree theories. In this work we give a general criterion of properies of multimaps, congenial to the just mentioned property of Fredholm maps. The criterion is formulated in the form of two theorems: direct and converse.

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