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Powers of countable Fréchet spaces

Volume 245 / 2019

Yinhe Peng, Stevo Todorcevic Fundamenta Mathematicae 245 (2019), 39-54 MSC: 54D55, 03E75. DOI: 10.4064/fm556-4-2018 Published online: 2 January 2019

Abstract

We examine problems of Galvin and Nogura about preservation of the Fréchet property when taking finite or countably infinite powers of countable topological spaces and groups. It is well known that adding the requirement that the topologies of the given countable spaces are analytic avoids many of the pathologies in this area. Here we show that a set-theoretic principle about open graphs could serve a similar purpose. For example, we show using this principle that if for some $n\geq 2$ the power $X^n$ of a countable space is Fréchet then so is $X^{n+1}$ provided it is sequential. We also give an example showing that in some sense this result is optimal.

Authors

  • Yinhe PengDepartment of Mathematics
    University of Toronto
    Toronto, Ontario, Canada, M5S 2E4
    e-mail
  • Stevo TodorcevicDepartment of Mathematics
    University of Toronto
    Toronto, Ontario, Canada, M5S 2E4
    e-mail

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