There is a paracompact Q-set space in ZFC

Author:
Zoltan T. Balogh

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1827-1833

MSC (1991):
Primary 54Dxx

DOI:
https://doi.org/10.1090/S0002-9939-98-04426-8

MathSciNet review:
1459106

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct a paracompact space such that every subset of is an -set, yet is not -discrete. We will construct our space not to have a -diagonal, which answers questions of A.V. Arhangel'skii and D. Shakhmatov on cleavable spaces.

**[A1]**A.V. Arhangel'skii,*The general concept of cleavability of a topological space*, Top. Applications**44**(1992), 27-36. MR**93k:54047****[A2]**A.V. Arhangel'skii,*Divisibility and cleavability of spaces*, Recent Developments of General Topology and Applications, Math. Res., vol. 67, Akademie-Verlag, Berlin, 1992, pp. 13-26. MR**94e:54028****[AS]**A.V. Arhangel'skii and D. Shakhmatov,*Pointwise approximation of arbitrary functions by countable families of continuous functions*, Trudy Sem. Petrovsk**13**(1988), 206-227; English transl., J. Soviet Math.**50**(1990), 1497-1511. MR**89m:41023****[B]**Z. Balogh,*There is a Q-set space in ZFC*, Proc. AMS**113**(1991), 557-561. MR**91m:54046****[BJ]**Z. Balogh and H. Junnila,*Totally analytic spaces under*, Proc. Amer. Math. Soc.**87**(1983), 519-527. MR**84j:54026****[C]**P. deCaux,*A nondegenerate -discrete Moore space which is connected*, Colloq. Math.**41**(1979), 207-209. MR**81m:54058****[H]**R.W. Hansell,*Some consequences of in the theory of analytic sets*, Proc. Amer. Math. Soc.**80**(1980), 311-319. MR**81j:54058****[J]**H. Junnila,*Some topological consequences of the Product Measure Extension Axiom*, Fund. Math.**115**(1983), 1-8. MR**85e:54021****[KV]**K. Kunen and J. Vaughan, eds.,*Handbook of Set-Theoretic Topology*, North-Holland, 1984. MR**85k:54001****[R]**G.M. Reed,*On normality and countable paracompactness*, Fund. Math**110**(1980), 145-152. MR**82d:54033**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
54Dxx

Retrieve articles in all journals with MSC (1991): 54Dxx

Additional Information

**Zoltan T. Balogh**

Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45058

Email:
ZTBalogh@miavx1.muohio.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04426-8

Keywords:
Paracompact,
Q-set space,
$G_{\delta }$-diagonal,
cleavable

Received by editor(s):
August 24, 1995

Additional Notes:
Research supported by NSF Grant DMS-9108476.

Communicated by:
Franklin D. Tall

Article copyright:
© Copyright 1998
American Mathematical Society