Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A Lindelöf space with no Lindelöf subspace of size $\aleph_1$

Author(s): Piotr Koszmider; Franklin D. Tall
Journal: Proc. Amer. Math. Soc. 130 (2002), 2777-2787.
MSC (2000): Primary 54A20, 54A25, 54A35; Secondary 03E35
Posted: March 13, 2002
MathSciNet review: 1900885
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: A consistent example of an uncountable Lindelöf $T_3$ (and hence normal) space with no Lindelöf subspace of size $\aleph_1$is constructed. It remains unsolved whether extra set-theoretic assumptions are necessary for the existence of such a space. However, our space has size $\aleph_2$and is a $P$-space, i.e., $G_\delta$'s are open, and for such spaces extra set-theoretic assumptions turn out to be necessary.

References:

[A]
A. Arhangel'ski{\v{\i}}\kern.15em; On the cardinality of bicompacta satisfying the first axiom of countability; Soviet Math. Dokl. 10, 1969, pp. 951 - 955.

[BT]
J. E. Baumgartner, F. D. Tall; Reflecting Lindelöfness; Top. Appl. In press.
[vD]
E. Van Douwen; The Integers and Topology; in [KV] pp. 111 - 167. MR 87f:54008

[E]
R. Engelking; General Topology; Heldermann Verlag, Berlin 1989. MR 91c:54001

[G]
I. Gorelic; The Baire category and forcing large Lindelöf spaces with points $G_\delta$; Proc. Amer. Math. Soc. 118, 1993, No 2. pp. 603-607. MR 93g:03046

[HJ]
A. Hajnal, I. Juhász; Remarks on the cardinality of compact spaces and their Lindelöf subspaces; Proc. Amer. Math. Soc. 59, 1976, pp. 146 - 148. MR 54:11263

[JW]
I. Juhász, W. Weiss; On a problem of Sikorski; Fund. Math. 100, 1978, pp. 223 - 227. MR 80g:54006

[JuW]
W. Just, M. Weese; Discovering Modern Set-Theory. Set-theoretic tools for every mathematician. Vol II. Graduate Studies in Mathematics. Vol 18. American Mathematical Society, Providence, RI, 1997. MR 99b:03001

[K]
K.Kunen; Set Theory; An Introduction to Independence Proofs; North Holland, 1983. MR 85e:03003

[KV]
K. Kunen, J. Vaughan eds. Handbook of set-theoretic topology; North Holland, 1984. MR 85k:54001

[R]
M. E. Rudin; Lectures on Set-Theoretic Topology; American Mathematical Society, Providence, 1975. MR 51:4128

[S]
S. Shelah; On some problems in general topology pp. 91 - 101, in Set Theory; Boise, Idaho; 1992 - 1994; American Mathematical Society; Providence 1996. MR 96k:03120

[T]
S.Todorcevic; Trees, subtrees and order types; Ann. Math. Logic 20, 1981, pp. 233-268. MR 82m:03062

[W]
W. Weiss; Versions of Martin's Axiom; in [KV] pp. 827 - 886. MR 86h:03088

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54A20, 54A25, 54A35, 03E35

Retrieve articles in all Journals with MSC (2000): 54A20, 54A25, 54A35, 03E35

Additional Information:

Piotr Koszmider
Affiliation: Departamento de Matemática, Universidade de São Paulo, Caixa Postal: 66281, São Paulo, SP, CEP: 05315-970, Brasil
Email: piotr@ime.usp.br

Franklin D. Tall
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: tall@math.toronto.edu

DOI: 10.1090/S0002-9939-02-06367-0
PII: S 0002-9939(02)06367-0
Keywords: Lindel\"of, nonreflection
Received by editor(s): December 12, 2000
Received by editor(s) in revised form: April 2, 2001
Posted: March 13, 2002
Additional Notes: Both authors were partially supported by the second author's grant A-7354 from the Natural Sciences and Engineering Research Council of Canada
Communicated by: Alan Dow
Copyright of article: Copyright 2002, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia