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

DOI:
https://doi.org/10.1090/S0002-9939-99-04783-8

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 , and every strongly discretely Lindelöf Tychonoff space of countable tightness is Lindelöf.

**[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]**A. V. Arhangel′skii,*A generic theorem in the theory of cardinal invariants of topological spaces*, Comment. Math. Univ. Carolin.**36**(1995), no. 2, 303–325. MR**1357532****[5]**Ryszard Engelking,*General topology*, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR**1039321****[6]**R. Hodel,*Cardinal functions. I*, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1–61. MR**776620****[7]**Mischenko A.S.,*Finally compact spaces*, Soviet Math. Dokl. 145 (1962), 1199-1202.**[8]**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:
https://doi.org/10.1090/S0002-9939-99-04783-8

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