A note on transitively D-spaces

作者：Peng Liang Xue^*

来源：Czechoslovak Mathematical Journal, 2011, 61(4): 1049-1061.

DOI：10.1007/s10587-011-0047-5

• transitively D
• sequential
• discretely Lindelof
• wcs-network

In this note, we show that if for any transitive neighborhood assignment phi for X there is a point-countable refinement F such that for any non-closed subset A of X there is some V a F such that |V a (c) A| a (c) 3/4 omega, then X is transitively D. As a corollary, if X is a sequential space and has a point-countable wcs*-network then X is transitively D, and hence if X is a Hausdorff k-space and has a point-countable k-network, then X is transitively D. We prove that if X is a countably compact sequential space and has a pointcountable wcs*-network, then X is compact. We point out that every discretely Lindelof space is transitively D. Let (X, tau) be a space and let (X, a") be a butterfly space over (X, tau). If (X, tau) is Fr,chet and has a point-countable wcs*-network (or is a hereditarily meta-Lindelof space), then (X, a") is a transitively D-space.

• 出版日期2011-12
• 单位北京工业大学