A simple Efimov space with sequentially-nice space of probability measures

Taras Banakh, Saak Gabriyelyan

Research output: Working paper/PreprintPreprint

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Abstract

Under Jensen's diamond principle $\diamondsuit$, we construct a simple Efimov space $K$ whose space of nonatomic probability measures $P_{na}(K)$ is first-countable and sequentially compact. These two properties of $P_{na}(K)$ imply that the space of probability measures $P(K)$ on $K$ is selectively sequentially pseudocompact and the Banach space $C(K)$ of continuous functions on $K$ has the Gelfand-Phillips property. We show also that any sequence of probability measures on $K$ that converges to an atomic measure converges in norm, and any sequence of probability measures on $K$ converging to zero in sup-norm has a subsequence converging to a nonatomic probability measure.
Original languageEnglish
StatePublished - 18 Oct 2021

Keywords

  • math.GN
  • math.FA
  • math.LO
  • 03E65, 28A33, 54A35, 54D30

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