Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Internal characterizations of productively Lindelöf spaces


Authors: Leandro F. Aurichi and Lyubomyr Zdomskyy
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 54D20, 54A35; Secondary 03E17
DOI: https://doi.org/10.1090/proc/14031
Published electronically: March 30, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present an internal characterization for the productively Lindelöf property, thus answering a long-standing problem attributed to Tamano. We also present some results about the relation ``Alster spaces'' vs. ``productively Lindelöf spaces''.


References [Enhancements On Off] (What's this?)

  • [1] Ofelia T. Alas, Leandro F. Aurichi, Lúcia R. Junqueira, and Franklin D. Tall, Non-productively Lindelöf spaces and small cardinals, Houston J. Math. 37 (2011), no. 4, 1373-1381. MR 2875278
  • [2] K. Alster, On the class of all spaces of weight not greater than $ \omega_1$ whose Cartesian product with every Lindelöf space is Lindelöf, Fund. Math. 129 (1988), no. 2, 133-140. MR 959437
  • [3] Witold Hurewicz, Über eine Verallgemeinerung des Borelschen Theorems, Math. Z. 24 (1926), no. 1, 401-421 (German). MR 1544773
  • [4] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375-376. MR 0152985
  • [5] J. Tatch Moore, Some of the combinatorics related to Michael's problem, Proc. Amer. Math. Soc. 127 (1999), no. 8, 2459-2467. MR 1486743
  • [6] Teodor C. Przymusiński, Products of normal spaces, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 781-826. MR 776637
  • [7] Dušan Repovš and Lyubomyr Zdomskyy, On the Menger covering property and $ D$-spaces, Proc. Amer. Math. Soc. 140 (2012), no. 3, 1069-1074. MR 2869091
  • [8] Marion Scheepers, Combinatorics of open covers. I. Ramsey theory, Topology Appl. 69 (1996), no. 1, 31-62. MR 1378387
  • [9] Franklin D. Tall, Lindelöf spaces which are Menger, Hurewicz, Alster, productive, or $ D$, Topology Appl. 158 (2011), no. 18, 2556-2563. MR 2847328

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 54D20, 54A35, 03E17

Retrieve articles in all journals with MSC (2010): 54D20, 54A35, 03E17


Additional Information

Leandro F. Aurichi
Affiliation: Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, São Carlos, SP, 13560-970, Brazil
Email: aurichi@icmc.usp.br

Lyubomyr Zdomskyy
Affiliation: Kurt Goedel Research Center for Mathematical Logic, University of Vienna, Waehringer Strasse 25, A-1090 Wien, Austria
Email: lzdomsky@gmail.com

DOI: https://doi.org/10.1090/proc/14031
Keywords: (Productively) Lindel\"of space, Alster space, Michael space, Menger property.
Received by editor(s): April 12, 2017
Received by editor(s) in revised form: October 18, 2017
Published electronically: March 30, 2018
Additional Notes: The first author was partially supported by FAPESP (2013/05469-7 and 2015/25725). A part of the results were obtained during the visit of the first author to the Kurt Gödel Center at the University of Vienna in January, 2017, partially supported by the FWF Grant M 1851-N35.
The second author would like to thank the Austrian Science Fund FWF (Grants I 1209-N25 and I 2374-N35) for generous support for this research.
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society