Covering properties in countable products, II

Sachio Higuchi; Hidenori Tanaka

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 491-502
  • ISSN: 0010-2628

Abstract

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In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If Y is a perfect subparacompact space and { X n : n ∈ ω } is a countable collection of subparacompact Čech-scattered spaces, then the product Y × ∏ n ∈ ω X n is subparacompact and (2) If { X n : n ∈ ω } is a countable collection of metacompact Čech-scattered spaces, then the product ∏ n ∈ ω X n is metacompact.

How to cite

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Higuchi, Sachio, and Tanaka, Hidenori. "Covering properties in countable products, II." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 491-502. <http://eudml.org/doc/249879>.

@article{Higuchi2006,
abstract = {In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and $\lbrace X_n : n\in \omega \rbrace $ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y\times \prod _\{n\in \omega \}X_n$ is subparacompact and (2) If $\lbrace X_n : n\in \omega \rbrace $ is a countable collection of metacompact Čech-scattered spaces, then the product $\prod _\{n\in \omega \}X_n$ is metacompact.},
author = {Higuchi, Sachio, Tanaka, Hidenori},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {countable product; C-scattered; Čech-scatterd; subparacompact; metacompact; countable product; C-scattered; Čech-scatterd; subparacompact; metacompact},
language = {eng},
number = {3},
pages = {491-502},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Covering properties in countable products, II},
url = {http://eudml.org/doc/249879},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Higuchi, Sachio
AU - Tanaka, Hidenori
TI - Covering properties in countable products, II
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 491
EP - 502
AB - In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and $\lbrace X_n : n\in \omega \rbrace $ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y\times \prod _{n\in \omega }X_n$ is subparacompact and (2) If $\lbrace X_n : n\in \omega \rbrace $ is a countable collection of metacompact Čech-scattered spaces, then the product $\prod _{n\in \omega }X_n$ is metacompact.
LA - eng
KW - countable product; C-scattered; Čech-scatterd; subparacompact; metacompact; countable product; C-scattered; Čech-scatterd; subparacompact; metacompact
UR - http://eudml.org/doc/249879
ER -

References

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  10. Tanaka H., Submetacompactness and weak submetacompactness in countable products, Topology Appl. 67 (1995), 29-41. (1995) Zbl0835.54021MR1360216
  11. Tanaka H., Submetacompactness in countable products, Topplogy Proc. 27 (2003), 307-316. (2003) Zbl1075.54006MR2048940
  12. Telgársky R., C-scattered and paracompact spaces, Fund. Math. 73 (1971), 59-74. (1971) MR0295293
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