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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On linearly Lindelöf and strongly
discretely Lindelöf spaces


Authors: A. V. Arhangel'skii and R. Z. Buzyakova
Journal: Proc. Amer. Math. Soc. 127 (1999), 2449-2458
MSC (1991): Primary 54A25; Secondary 54A35
Published electronically: April 8, 1999
MathSciNet review: 1487356
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed $2^{\omega }$, and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.


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

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Additional Information

A. V. Arhangel'skii
Affiliation: July–December: Department of Mathematics, Moscow State University, Moscow 119899, Russia; January–June: Department of Mathematics, Ohio State University, Athens, Ohio 45701
Email: arhangel@nw.math.msu.su, arhangel@bing.math.ohiou.edu

R. Z. Buzyakova
Affiliation: Chair of General Topology and Geometry, Mech.-Math. Faculty, Moscow State University, Moscow 119899, Russia
Email: raushan@shade.msu.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04783-8
PII: S 0002-9939(99)04783-8
Keywords: Lindel\"{o}f space, linearly Lindel\"{o}f space, free sequence, $G_{2^{\omega }}$-set, first countability, complete accumulation point
Received by editor(s): June 27, 1997
Received by editor(s) in revised form: October 27, 1997
Published electronically: April 8, 1999
Additional Notes: The first author was partially supported by NSF-grant DMS–9312363
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society