On linearly Lindelöf and strongly discretely Lindelöf spaces
Authors:
A. V. Arhangel'skii and R. Z. Buzyakova
Journal:
Proc. Amer. Math. Soc. 127 (1999), 24492458
MSC (1991):
Primary 54A25; Secondary 54A35
Published electronically:
April 8, 1999
MathSciNet review:
1487356
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: We prove that the cardinality of every first countable linearly Lindelöf Tychonoff space does not exceed , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.
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 Alexandroff P.S. and P.S. Urysohn, Memoire sur les espaces topologiques compacts, Nederl. Akad. Wetensch. Proc. Ser. A, 14 (1929), 196.
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 Arhangel'skii A.V., On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951955.
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 Arhangel'skii A.V., Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978), 3396.
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 Rudin M.E., Some Conjectures, in: J. van Mill and G.M Reed, Editors, Open Problems in Topology (1990), 184193, NorthHolland, Amsterdam. CMP 91:03
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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/S0002993999047838
PII:
S 00029939(99)047838
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 NSFgrant DMS–9312363
Communicated by:
Alan Dow
Article copyright:
© Copyright 1999
American Mathematical Society
