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A survey on topological games and their applications in analysis.

Jiling Cao, Warren B. Moors (2006)

RACSAM

In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.

A suspension theorem for the proper homotopy and strong shape theories

C. Elvira-Donazar, L. J. Hernandez-Paricio (1995)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

A technique for constructing examples

van Douwen, Eric K. (1977)

General topology and its relations to modern analysis and algebra IV

A theorem of Borsuk-Ulam type for multifunctions

M. Ehrlich (1979)

Fundamenta Mathematicae

A theorem of Meir-Keeler type revisited.

Cho, Y.J., Murthy, P.P., Jungck, G. (2000)

International Journal of Mathematics and Mathematical Sciences

A theorem of Šarkovskii characterizing continuous maps of zero topological entropy

Katarína Janková, Jaroslav Smítal (1989)

Mathematica Slovaca

A theorem of Stone-Čech type, and a theorem of Tychonoff type, without the axiom of choice; and their realcompact analogues

W. W. Comfort (1968)

Fundamenta Mathematicae

A Theorem of the Closed Graph Type.

Vlastimil Pták (1974)

Manuscripta mathematica

A theorem of the Hahn-Banach type and its applications

Zbigniew Gajda, Andrzej Smajdor, Wilhelmina Smajdor (1992)

Annales Polonici Mathematici

Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.