Fixed Point Theory in Multiply Ordered Spaces

摘要

The underlying paper contains the demonstration of a Knaster-Kuratowski-Mazurkiewicz-type theorem within the setting of multiply ordered spaces. A multiply ordered space is a topological space supplied with a finite number of continuous complete orderings. The author uses these orderings to define a simplicial subdivision-resembling structure on the space involved, in an explicit manner. Also, the orderings give rise to a combinatorial boundary concept and to a new type of convexity. The results are even valid in some non metrizable spaces. Applied within the context of Euclidean space, the author obtains a statement much stronger than the classical Knaster-Kuratowski-Mazurkiewicz theorem. (Copyright (c) 1989 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)