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On the resolvability of locally connected spaces
Author(s):
Camillo
Costantini
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1861-1864.
MSC (2000):
Primary 54D05, 54D10;
Secondary 54A25
Posted:
November 19, 2004
MathSciNet review:
2120288
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Abstract:
We solve a problem of Padmavally about resolvability of locally connected spaces, in the case where the space under consideration is regular.
References:
-
- [AC]
- A. V. Arhangel'skii and P. J. Collins, On submaximal spaces, Topology Appl. 64 (1995), 219-241. MR 1342519 (96m:54002)
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- R. Engelking, General Topology. Revised and completed edition, Sigma Series in Pure Mathematics, n. 6, Heldermann Verlag, Berlin, 1989. MR 1039321 (91c:54001)
- [He]
- E. Hewitt, A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309-333. MR 0008692 (5:46e)
- [Pad]
- K. Padmavally, An example of a connected irresolvable Hausdorff space, Duke Math. J. 20 (1953), 513-520. MR 0059539 (15:546g)
- [Pav]
- O. Pavlov, On resolvability of topological spaces, Topology Appl. 126 (2002), 37-47. MR 1934251 (2003h:54002)
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- P. Simon, An example of maximal connected Hausdorff space, Fund. Math. 100 (1978), 157-163. MR 0487978 (58:7557)
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Additional Information:
Camillo
Costantini
Affiliation:
Department of Mathematics, University of Torino, via Carlo Alberto 10, 10123 Torino, Italy
Email:
costanti@dm.unito.it
DOI:
10.1090/S0002-9939-04-07682-8
PII:
S 0002-9939(04)07682-8
Keywords:
Resolvable space,
locally connected space,
connected space,
regular space,
$\pi$-base
Received by editor(s):
February 4, 2003
Received by editor(s) in revised form:
February 16, 2004
Posted:
November 19, 2004
Communicated by:
Alan Dow
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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