Every Filter is Homeomorphic to Its Square

Volume 64 / 2016

Andrea Medini, Lyubomyr Zdomskyy Bulletin Polish Acad. Sci. Math. 64 (2016), 63-67 MSC: 54H99, 54E99, 03E05. DOI: 10.4064/ba8065-6-2016 Published online: 8 July 2016

Abstract

We show that every filter $\mathcal {F}$ on $\omega $, viewed as a subspace of $2^\omega $, is homeomorphic to $\mathcal {F}^2$. This generalizes a theorem of van Engelen, who proved that this holds for Borel filters.

Authors

  • Andrea MediniKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    Währinger Straße 25
    A-1090 Wien, Austria
    e-mail
  • Lyubomyr ZdomskyyKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    Währinger Straße 25
    A-1090 Wien, Austria
    e-mail

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