Hyperspaces and the S-equivariant Complete Invariance Property

Maury, Saurabh Chandra

  • Received : 2013.03.24
  • Accepted : 2014.04.21
  • Published : 2015.03.23


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.


Equivariant map;Hyperspaces;Hausdorff metric;CIP;CIPH


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Supported by : CSIR