West’s problem on equivariant hyperspaces and Banach-Mazur compacta

@article{Antonyan2003WestsPO,
  title={West’s problem on equivariant hyperspaces and Banach-Mazur compacta},
  author={S. Antonyan},
  journal={Transactions of the American Mathematical Society},
  year={2003},
  volume={355},
  pages={3379-3404}
}
  • S. Antonyan
  • Published 2003
  • Mathematics, Geography
  • Transactions of the American Mathematical Society
Let G be a compact Lie group, X a metric G-space, and exp X the hyperspace of all nonempty compact subsets of X endowed with the Hausdorff metric topology and with the induced action of G. We prove that the following three assertions are equivalent: (a) X is locally continuum-connected (resp., connected and locally continuum-connected); (b) expX is a G-ANR (resp., a G-AR); (c) (exp X)/G is an ANR (resp., an AR). This is applied to show that (expG)/G is an ANR (resp., an AR) for each compact… Expand

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