### The Knaster-Kuratowski-Mazurkiewicz theorem and almost fixed points

DOI: http://dx.doi.org/10.12775/TMNA.2000.038

#### Abstract

From the KKM theorem for the ``closed'' and ``open'' valued cases,

we deduce a generalization of the Alexandroff-Pasynkoff theorem,

existence theorems for almost fixed points of lower semicontinuous multimaps,

and a partial solution of the Ben-El-Mechaiekh conjecture.

we deduce a generalization of the Alexandroff-Pasynkoff theorem,

existence theorems for almost fixed points of lower semicontinuous multimaps,

and a partial solution of the Ben-El-Mechaiekh conjecture.

#### Keywords

Topological vector space (t.v.s.); KKM theorem; almost convex subset; almost fixed point; lower semicontinuous (l.s.c.) map; upper semi-continuous (u.s.c.) map; fixed point

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