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The union of two $D$-spaces need not be $D$

Volume 220 / 2013

Dániel T. Soukup, Paul J. Szeptycki Fundamenta Mathematicae 220 (2013), 129-137 MSC: Primary 54D20; Secondary 54A35, 54G20. DOI: 10.4064/fm220-2-3

Abstract

We construct from $\diamondsuit $ a $T_2$ example of a hereditarily Lindelöf space $X$ that is not a $D$-space but is the union of two subspaces both of which are $D$-spaces. This answers a question of Arhangel'skii.

Authors

  • Dániel T. SoukupDepartment of Mathematics
    University of Toronto
    Toronto, ON, M5S 1A1 Canada
    e-mail
  • Paul J. SzeptyckiDepartment of Mathematics and Statistics
    York University
    Toronto, ON, M3J 1P3 Canada
    e-mail

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