[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2015.55.1.219

Hyperspaces and the S-equivariant Complete Invariance Property

Maury, Saurabh Chandra (Department of Mathematics, University of Allahabad)

Publication Information

Kyungpook Mathematical Journal / v.55, no.1, 2015 , pp. 219-224 More about this Journal

Abstract

In this paper it is investigated as to when a nonempty invariant closed subset A of a $S^1$ -space X containing the set of stationary points (S) can be the fixed point set of an equivariant continuous selfmap on X and such space X is said to possess the S-equivariant complete invariance property (S-ECIP). It is also shown that if X is a metric space and $S^1$ acts on $X{\times}S^1$ by the action $(x,p){\cdot}q=(x,p{\cdot}q)$ , where p, $q{\in}S^1$ and $x{\in}X$ , then the hyperspace $2^{X{\times}S^1}$ of all nonempty compact subsets of $X{\times}S^1$ has the S-ECIP.

Keywords

Equivariant map; Hyperspaces; Hausdorff metric; CIP; CIPH;

Citations & Related Records

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