A note on the extent of two subclasses of star countable spaces

2012 ◽  
Vol 10 (3) ◽  
pp. 1067-1070 ◽  
Author(s):  
Zuoming Yu
Keyword(s):  
Star Countable

On star Lindelöf spaces

2020 ◽  
Vol 57 (2) ◽  
pp. 139-146
Author(s):  
Wei-Feng Xuan ◽  
Yan-Kui Song
Keyword(s):  
Hausdorff Space ◽  
Normal Space ◽  
Star Countable

AbstractIn this paper, we prove that if X is a space with a regular Gδ-diagonal and X2 is star Lindelöf then the cardinality of X is at most 2c. We also prove that if X is a star Lindelöf space with a symmetric g-function such that {g2(n, x): n ∈ ω} = {x} for each x ∈ X then the cardinality of X is at most 2c. Moreover, we prove that if X is a star Lindelöf Hausdorff space satisfying Hψ(X) = κ then e(X) 22κ; and if X is Hausdorff and we(X) = Hψ(X) = κsubset of a space then e(X) 2κ. Finally, we prove that under V = L if X is a first countable DCCC normal space then X has countable extent; and under MA+¬CH there is an example of a first countable, DCCC and normal space which is not star countable extent. This gives an answer to the Question 3.10 in Spaces with property (DC(ω1)), Comment. Math. Univ. Carolin., 58(1) (2017), 131-135.

scholarly journals Characterizations of Strongly Paracompact Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Xin Zhang
Keyword(s):  
Open Cover ◽  
Normal Space ◽  
Compact Spaces ◽  
Countably Paracompact ◽  
Star Countable ◽  
Perfectly Normal Space ◽  
Paracompact Spaces ◽  
Perfectly Normal

Characterizations of strongly compact spaces are given based on the existence of a star-countable open refinement for every increasing open cover. It is proved that a countably paracompact normal space (a perfectly normal space or a monotonically normal space) is strongly paracompact if and only if every increasing open cover of the space has a star-countable open refinement. Moreover, it is shown that a space is linearlyDprovided that every increasing open cover of the space has a point-countable open refinement.

scholarly journals Spaces with star countable extent

2016 ◽  
Vol 57 (3) ◽  
pp. 381-395 ◽  
Author(s):  
 Rojas-Sánchez A. D. ◽  
Tamariz-Mascarúa Á.
Keyword(s):  
Star Countable

scholarly journals A Positive Answer to Velichko's Question

2006 ◽  
Vol 13 (2) ◽  
pp. 291-296
Author(s):  
Jinjin Li ◽  
Zhaowen Li
Keyword(s):  
Metric Space ◽  
Positive Answer ◽  
Star Countable ◽  
Separable Metric Space

Abstract We give positive answer to Velichko's question in which the quotient and 𝑠-map is replaced by a sequence-covering and 𝑐𝑠-map. In addition, let 𝑋 have a star-countable 𝑘-network, then 𝑋 is a sequence-covering and 𝑐𝑠-image of a locally separable metric space if and only if 𝑋 is a sequencecovering and 𝑐𝑠-image of a metric space.

A NOTE ON SPACES WITH RANK 2-DIAGONAL

2014 ◽  
Vol 90 (1) ◽  
pp. 141-143 ◽  
Author(s):  
WEI-FENG XUAN ◽  
WEI-XUE SHI
Keyword(s):  
Chain Condition ◽  
Countable Chain Condition ◽  
Countable Chain ◽  
Star Countable ◽  
Rank 2

AbstractWe 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 $\mathfrak{c}$.

scholarly journals Spaces with a star-countable k-network, and related results

1996 ◽  
Vol 74 (1-3) ◽  
pp. 25-38 ◽  
Author(s):  
Chuan Liu ◽  
Yoshio Tanaka
Keyword(s):  
Star Countable

Star countable spaces and $$\omega $$ ω -domination of discrete subspaces

2018 ◽  
Vol 113 (2) ◽  
pp. 807-818 ◽  
Author(s):  
Ofelia T. Alas ◽  
Lucia R. Junqueira ◽  
Vladimir V. Tkachuk ◽  
Richard G. Wilson
Keyword(s):  
Star Countable

Some remarks on almost star countable spaces

2015 ◽  
Vol 52 (1) ◽  
pp. 12-20
Author(s):  
Yan-Kui Song
Keyword(s):  
Open Cover ◽  
Countable Subset ◽  
Topological Properties ◽  
Star Countable

A space X is almost star countable (weakly star countable) if for each open cover U of X there exists a countable subset F of X such that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\bigcup {_{x \in F}\overline {St\left( {x,U} \right)} } = X$ \end{document} (respectively, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\overline {\bigcup {_{x \in F}} St\left( {x,U} \right)} = X$ \end{document}. In this paper, we investigate the relationships among star countable spaces, almost star countable spaces and weakly star countable spaces, and also study topological properties of almost star countable spaces.

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