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On linearly Lindelöf and strongly discretely Lindelöf spaces
Author(s):
A.
V.
Arhangel'skii;
R.
Z.
Buzyakova
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2449-2458.
MSC (1991):
Primary 54A25;
Secondary 54A35
Posted:
April 8, 1999
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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.
References:
- [1]
- Alexandroff P.S. and P.S. Urysohn, Memoire sur les espaces topologiques compacts, Nederl. Akad. Wetensch. Proc. Ser. A, 14 (1929), 1-96.
- [2]
- Arhangel'skii A.V., On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951-955.
- [3]
- Arhangel'skii A.V., Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978), 33-96.
- [4]
- Arhangel'skii A.V., A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carolinae 36:2 (1995), 303-325. MR 97b:54005
- [5]
- Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. MR 91c:54001
- [6]
- Hodel R.E., Cardinal Functions, 1, in: Handbook of Set-theoretic Topology, Editors: K. Kunen and J.E. Vaughan, Chapter 1, 1-62, North-Holland, Amsterdam, 1984. MR 86j:54007
- [7]
- Mischenko A.S., Finally compact spaces, Soviet Math. Dokl. 145 (1962), 1199-1202.
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- Rudin M.E., Some Conjectures, in: J. van Mill and G.M Reed, Editors, Open Problems in Topology (1990), 184-193, North-Holland, 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:
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
Posted:
April 8, 1999
Additional Notes:
The first author was partially supported by NSF-grant DMS--9312363
Communicated by:
Alan Dow
Copyright of article:
Copyright
1999,
American Mathematical Society
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