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Extensions of perfect GO-spaces and  -discrete dense sets
Author(s):
Wei-Xue
Shi
Journal:
Proc. Amer. Math. Soc.
127
(1999),
615-618.
MSC (1991):
Primary 54F05, 54D35;
Secondary 54F65, 54A10.
MathSciNet review:
1468203
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Abstract:
In this paper, we prove that if a perfect GO-space  has a  -discrete dense set, then  has a perfect linearly ordered extension. This answers a problem raised by H. R. Bennett, D. J. Lutzer and S. Purisch. And the result is also a partial answer to an old problem posed by H. R. Bennett and D. J. Lutzer.
References:
- 1.
- H. R. Bennett and D. J. Lutzer, Problems in perfect ordered space, in: J. van Mill and G. M. Reed, eds, Open Problems in Topology (North-Holland, Amsterdam, 1990), 223-236. CMP 91:03
- 2.
- H. R. Bennett, D. J. Lutzer and S. D. Purisch, On dense subspaces of generalized ordered spaces, Topology Appl. (to appear).
- 3.
- R. Engelking, General Topology, (Heldermann, Berlin, rev.ed., 1989). MR 91c:54001
- 4.
- D. J. Lutzer, On generalized ordered spaces, Dissertationes Math. 89(1971). MR 48:3018
- 5.
- W.-X. Shi, Perfect GO-spaces which have a perfect linearly ordered extension, Topology Appl. 81 (1997), 23-33.
- 6.
- W.-X. Shi, T. Miwa and Y.-Z. Gao, A perfect GO-space which cannot densely embed in any perfect orderable space, Topology Appl. 66(1995), 241-249. MR 96i:54026
- 7.
- -, Any perfect GO-space with the underlying LOTS satisfying local perfectness can embed in a perfect LOTS, Topology Appl. 74(1996), 17-24. CMP 97:06
- 8.
- J. van Wouwe, GO-spaces and generalizations of metrizability, MC Tract no. 104, (Mathematical Center, Amsterdam, 1979). MR 80m:54046
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Additional Information:
Wei-Xue
Shi
Affiliation:
Department of Mathematics, Changchun Teachers College, Changchun 130032, China
Address at time of publication:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
Email:
shi@abel.math.tsukuba.ac.jp
DOI:
10.1090/S0002-9939-99-04554-2
PII:
S 0002-9939(99)04554-2
Keywords:
$\sigma$-discrete set,
perfect,
LOTS,
GO-space,
extension
Received by editor(s):
January 7, 1997
Received by editor(s) in revised form:
May 26, 1997
Communicated by:
Alan Dow
Copyright of article:
Copyright
1999,
American Mathematical Society
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