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2 results

  • A NOTE ON SPACES WITH RANK 2-DIAGONAL

  • Part of
  • WEI-FENG XUAN, WEI-XUE SHI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 90 / Issue 1 / August 2014
    Published online by Cambridge University Press:
    02 April 2014, pp. 141-143
    Print publication:
    August 2014
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  • We prove that if a space $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}X$ with a rank 2-diagonal either has the countable chain condition or is star countable then the cardinality of $X$ is at most $\mathfrak{c}$.

  • A PSEUDOCOMPACT TYCHONOFF SPACE THAT IS NOT STAR LINDELÖF

  • Part of
  • YANKUI SONG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 84 / Issue 3 / December 2011
    Published online by Cambridge University Press:
    21 July 2011, pp. 452-454
    Print publication:
    December 2011
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  • Let P be a topological property. A space X is said to be star P if whenever 𝒰 is an open cover of X, there exists a subspace A⊆X with property P such that X=St(A,𝒰), where St(A,𝒰)=⋃ {U∈𝒰:U∩A≠0̸}. In this paper we construct an example of a pseudocompact Tychonoff space that is not star Lindelöf, which gives a negative answer to Alas et al. [‘Countability and star covering properties’, Topology Appl.158 (2011), 620–626, Question 3].