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On the Menger covering property and $ D$-spaces

Authors: Dušan Repovš and Lyubomyr Zdomskyy
Journal: Proc. Amer. Math. Soc. 140 (2012), 1069-1074
MSC (2010): Primary 54D20, 54A35; Secondary 54H05, 03E17
Published electronically: July 6, 2011
MathSciNet review: 2869091
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Abstract | References | Similar Articles | Additional Information

Abstract: The main results of this paper are:

  • It is consistent that every subparacompact space $ X$ of size $ \omega_1$ is a $ D$-space.
  • If there exists a Michael space, then all productively Lindelöf spaces have the Menger property and, therefore, are $ D$-spaces.
  • Every locally $ D$-space which admits a $ \sigma$-locally finite cover by Lindelöf spaces is a $ D$-space.

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Additional Information

Dušan Repovš
Affiliation: Faculty of Mathematics and Physics, and Faculty of Education, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001

Lyubomyr Zdomskyy
Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, A-1090 Wien, Austria

Keywords: $D$-space, subparacompactness, Menger property, (productively) Lindelöf space, Michael space
Received by editor(s): September 28, 2010
Received by editor(s) in revised form: December 4, 2010, and December 13, 2010
Published electronically: July 6, 2011
Additional Notes: The first author was supported by SRA grants P1-0292-0101 and J1-2057-0101.
The second author acknowledges the support of FWF grant P19898-N18
The authors would also like to thank Leandro Aurichi, Franklin Tall, and Hang Zhang for kindly making their recent papers available to us.
Communicated by: Julia Knight
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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