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)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

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
Full-text PDF

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?)

  • [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.
  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54A25, 54A35

Retrieve articles in all journals with MSC (1991): 54A25, 54A35

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

American Mathematical Society