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2 results

  • A RESULT ON MONOTONICALLY LINDELÖF GENERALIZED ORDERED SPACES

  • Part of
  • AI-JUN XU, WEI-XUE SHI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 84 / Issue 3 / December 2011
    Published online by Cambridge University Press:
    18 August 2011, pp. 481-483
    Print publication:
    December 2011
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  • In this paper, we show that the character of any monotonically Lindelöf generalized ordered (GO) space is not greater than ω1, which gives a negative answer to a question posed by Levy and Matveev [‘Some questions on monotone Lindelöfness’, Questions Answers Gen. Topology26 (2008), 13–27, Question 51].

  • A NOTE ON PARACOMPACT p-SPACES AND THE MONOTONE D-PROPERTY

  • Part of
  • YIN-ZHU GAO, WEI-XUE SHI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 83 / Issue 3 / June 2011
    Published online by Cambridge University Press:
    07 February 2011, pp. 463-469
    Print publication:
    June 2011
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  • For any generalized ordered space X with the underlying linearly ordered topological space Xu, let X* be the minimal closed linearly ordered extension of X and be the minimal dense linearly ordered extension of X. The following results are obtained.

    1. (1) The projection mapping π:X*→X, π(〈x,i〉)=x, is closed.

    2. (2) The projection mapping , ϕ(〈x,i〉)=x, is closed.

    3. (3) X* is a monotone D-space if and only if X is a monotone D-space.

    4. (4) is a monotone D-space if and only if Xu is a monotone D-space.

    5. (5) For the Michael line M, is a paracompact p-space, but not continuously Urysohn.