|
A Moore space with a  -discrete  -base which cannot be densely embedded in any Moore space with the Baire property
Author(s):
David
L.
Fearnley
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3095-3100.
MSC (1991):
Primary 54D20, 54D25;
Secondary 54E52
Posted:
April 23, 1999
MathSciNet review:
1605960
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
The author answers a question raised in the literature about twenty five years ago and raised again more recently in Open Problems in Topology, by G. M. Reed, concerning the conjecture that every Moore space with a  -discrete  -base can be densely embedded in a Moore space having the Baire property. Even though closely related results have made this conjecture seem likely to be true, the author shows that, surprisingly, the conjecture is false.
References:
- 1.
- J. M. Aarts and D. J. Lutzer, Pseudo-completeness and the product of Baire spaces, Pacific J. Math. 48 (1), (1973), 1-10. MR 48:5009
- 2.
- R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175-186. MR 13:264f
- 3.
- M. E. Estill (Rudin), Concerning abstract spaces, Duke Math. J. 17 (1950), 317-327. MR 13:148b
- 4.
- B. Fitzpatrick, On dense subsets of Moore spaces II, Fund. Math. 61 (1967), 91-92. MR 36:2119
- 5.
- G. M. Reed, Concerning completable Moore spaces, Proc. Amer. Math. Soc. 36 (1972), 591-596. MR 46:8185
- 6.
- G. M. Reed, Lecture notes in mathematics, vol. 378, Springer-Verlag, 1972, pp. 368-384.
- 7.
- J. Van Mill and G. M. Reed (editors), Open problems in topology, North-Holland Publ., 1990, problem 303. MR 92c:54001
- 8.
- K. E. Whipple, Cauchy sequences in Moore spaces, Pacific J. Math. 18 (1966), 191-199. MR 33:4889
- 9.
- H. E. White, Jr., First countable spaces that have pseudo-bases, Canad. J. Math. Bull. 21 (1978), 103-112. MR 58:2675
- 10.
- J. N. Younglove, Concerning dense metric subspaces of certain non-metric spaces, Fund. Math. 48 (1959), 15-25. MR 22:1878
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
54D20, 54D25,
54E52
Retrieve articles in all Journals with
MSC (1991):
54D20, 54D25,
54E52
Additional Information:
David
L.
Fearnley
Affiliation:
Mathematics Institute, 24-29 St. Giles, Oxford University, Oxford OX1 3LB, England
Address at time of publication:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email:
david.fearnley@st-edmund-hall.oxford.ac.uk, davidf@math.byu.edu
DOI:
10.1090/S0002-9939-99-04876-5
PII:
S 0002-9939(99)04876-5
Keywords:
Moore space,
$\sigma$-discrete $\pi$-base,
Baire property,
embedding
Received by editor(s):
June 23, 1997
Received by editor(s) in revised form:
December 12, 1997
Posted:
April 23, 1999
Additional Notes:
This material is based on work supported under a National Science Foundation Graduate Fellowship
Communicated by:
Alan Dow
Copyright of article:
Copyright
1999,
American Mathematical Society
|
