Reflecting point-countable families

Author:
Zoltan T. Balogh

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1289-1296

MSC (2000):
Primary 54E35, 54A35, 54D20

DOI:
https://doi.org/10.1090/S0002-9939-02-06621-2

Published electronically:
July 25, 2002

MathSciNet review:
1948122

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if every -sized subspace of a (regular) space of density has a point-countable base, then so does . Similar results hold for meta-Lindelöfness. Dow's reflection theorem and a number of other results are deduced as corollaries and applications.

**[B83]**Z. Balogh,*Locally nice spaces under Martin's Axiom*, Comment. Math. Univ. Carolin.**24**(1983), 63-87. MR**85b:54005****[B]**Z. Balogh,*Locally nice spaces and Axiom*(to appear).**[D88]**A. Dow,*An empty class of nonmetric spaces*, Proc. Amer. Math. Soc.**104**(1988), 999-1001. MR**89j:54032****[D91]**A. Dow,*An introduction to applications of elementary submodels to topology*, Topology Proc.**13**(1988), 17-72. MR**91a:54003****[HV]**R.E. Hodel, J.E. Vaughan,*Reflection theorems for cardinal functions*, Topology Appl.**100**(2000), 47-66. MR**2001b:54004****[K]**K. Kunen,*Set theory*, North-Holland, 1980. MR**82f:03001**; Reprint MR**85e:03003****[KV]**K. Kunen and J.E. Vaughan, eds.,*Handbook of Set-theoretic Topology*, North-Holland, 1984. MR**85k:54001****[S]**S. Shelah,*Remarks on**-collectionwise Hausdorff spaces*, Topology Proc.**2**(1977), 583-592. MR**81f:03060****[V]**J.E. Vaughan,*On Dow's reflection theorem for metrizable spaces*, Topology Proc.**22**(1997), 351-361. MR**99m:54018**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
54E35,
54A35,
54D20

Retrieve articles in all journals with MSC (2000): 54E35, 54A35, 54D20

Additional Information

**Zoltan T. Balogh**

Affiliation:
Department of Mathematics & Statistics, Miami University, Oxford, Ohio 45056

Email:
baloghzt@muohio.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06621-2

Keywords:
Point-countable,
reflection

Received by editor(s):
July 31, 2001

Received by editor(s) in revised form:
November 2, 2001

Published electronically:
July 25, 2002

Communicated by:
Alan Dow

Article copyright:
© Copyright 2002
American Mathematical Society