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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Extensions of perfect GO-spaces and $\sigma$-discrete dense sets
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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
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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
  • 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