Fixed points for set-valued maps: A topological perspective (Q2753302)

In this paper a purely topological notion of space approximation, which contains the admissibility of Klee and accommodates recent topological notions of convexity, is defined. The large class of approximative neighborhood extension spaces are shown to have this approximation property. Then he derives a key fixed point principle for set-valued maps which not only allows the passage from basic domains to more elaborate ones but also permits the shifting of compactness from domains to maps. NEWLINENEWLINENEWLINEThe results unify a number of recent generalizations of the Kakutani-Fan-Himmelberg fixed point theorem and shed some light on the role of topology in fixed point theory for set-valued maps.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].