Extensions of perfect GO-spaces and $\sigma$-discrete dense sets
HTML articles powered by AMS MathViewer
- by Wei-Xue Shi PDF
- Proc. Amer. Math. Soc. 127 (1999), 615-618 Request permission
Abstract:
In this paper, we prove that if a perfect GO-space $X$ has a $\sigma$-discrete dense set, then $X$ 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
- 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.
- H. R. Bennett, D. J. Lutzer and S. D. Purisch, On dense subspaces of generalized ordered spaces, Topology Appl. (to appear).
- Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
- D. J. Lutzer, On generalized ordered spaces, Dissertationes Math. (Rozprawy Mat.) 89 (1971), 32. MR 324668
- W.-X. Shi, Perfect GO-spaces which have a perfect linearly ordered extension, Topology Appl. 81 (1997), 23–33.
- Wei Xue Shi, Takuo Miwa, and Yin Zhu Gao, A perfect GO-space which cannot densely embed in any perfect orderable space, Topology Appl. 66 (1995), no. 3, 241–249. MR 1359515, DOI 10.1016/0166-8641(95)00031-B
- —, Any perfect GO-space with the underlying LOTS satisfying local perfectness can embed in a perfect LOTS, Topology Appl. 74(1996), 17–24.
- J. M. van Wouwe, GO-spaces and generalizations of metrizability, Mathematical Centre Tracts, vol. 104, Mathematisch Centrum, Amsterdam, 1979. MR 541832
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
- Received by editor(s): January 7, 1997
- Received by editor(s) in revised form: May 26, 1997
- Communicated by: Alan Dow
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 615-618
- MSC (1991): Primary 54F05, 54D35; Secondary 54F65, 54A10
- DOI: https://doi.org/10.1090/S0002-9939-99-04554-2
- MathSciNet review: 1468203