Σ -products of paracompact Čech-scattered spaces

Hidenori Tanaka

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 1, page 127-140
  • ISSN: 0010-2628

Abstract

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In this paper, we shall discuss Σ -products of paracompact Čech-scattered spaces and show the following: (1) Let Σ be a Σ -product of paracompact Čech-scattered spaces. If Σ has countable tightness, then it is collectionwise normal. (2) If Σ is a Σ -product of first countable, paracompact (subparacompact) Čech-scattered spaces, then it is shrinking (subshrinking).

How to cite

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Tanaka, Hidenori. "$\Sigma $-products of paracompact Čech-scattered spaces." Commentationes Mathematicae Universitatis Carolinae 47.1 (2006): 127-140. <http://eudml.org/doc/249871>.

@article{Tanaka2006,
abstract = {In this paper, we shall discuss $\Sigma $-products of paracompact Čech-scattered spaces and show the following: (1) Let $\Sigma $ be a $\Sigma $-product of paracompact Čech-scattered spaces. If $\Sigma $ has countable tightness, then it is collectionwise normal. (2) If $\Sigma $ is a $\Sigma $-product of first countable, paracompact (subparacompact) Čech-scattered spaces, then it is shrinking (subshrinking).},
author = {Tanaka, Hidenori},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\Sigma $-product; C-scattered; Čech-scattered; paracompact; subparacompact; collectionwise normal; shrinking; subshrinking; countable tightness; -product; collectionwise normality; shrinking; paracompact; scattered},
language = {eng},
number = {1},
pages = {127-140},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\Sigma $-products of paracompact Čech-scattered spaces},
url = {http://eudml.org/doc/249871},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Tanaka, Hidenori
TI - $\Sigma $-products of paracompact Čech-scattered spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 1
SP - 127
EP - 140
AB - In this paper, we shall discuss $\Sigma $-products of paracompact Čech-scattered spaces and show the following: (1) Let $\Sigma $ be a $\Sigma $-product of paracompact Čech-scattered spaces. If $\Sigma $ has countable tightness, then it is collectionwise normal. (2) If $\Sigma $ is a $\Sigma $-product of first countable, paracompact (subparacompact) Čech-scattered spaces, then it is shrinking (subshrinking).
LA - eng
KW - $\Sigma $-product; C-scattered; Čech-scattered; paracompact; subparacompact; collectionwise normal; shrinking; subshrinking; countable tightness; -product; collectionwise normality; shrinking; paracompact; scattered
UR - http://eudml.org/doc/249871
ER -

References

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  12. Rudin M.E., The shrinking property, Canad. Math. Bull. 28 (1983), 385-388. (1983) Zbl0536.54013MR0716576
  13. Tanaka H., Yajima Y., Σ -products of paracompact C-scattered spaces, Topology Appl. 124 (2002), 39-46. (2002) MR1926133
  14. Telgársky R., C-scattered and paracompact spaces, Fund. Math. 73 (1971), 59-74. (1971) MR0295293
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  16. Yajima Y., The shrinking property of Σ -products, Tsukuba J. Math. 13 (1989), 83-98. (1989) Zbl0697.54006MR1003593

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