Order-like structure of monotonically normal spaces

Scott W. Williams; Hao Xuan Zhou

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 207-217
  • ISSN: 0010-2628

Abstract

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For a compact monotonically normal space X we prove:   (1)   X has a dense set of points with a well-ordered neighborhood base (and so X is co-absolute with a compact orderable space);   (2)   each point of X has a well-ordered neighborhood π -base (answering a question of Arhangel’skii);   (3)   X is hereditarily paracompact iff X has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal spaces.

How to cite

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Williams, Scott W., and Zhou, Hao Xuan. "Order-like structure of monotonically normal spaces." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 207-217. <http://eudml.org/doc/248276>.

@article{Williams1998,
abstract = {For a compact monotonically normal space X we prove:   (1)   $X$ has a dense set of points with a well-ordered neighborhood base (and so $X$ is co-absolute with a compact orderable space);   (2)   each point of $X$ has a well-ordered neighborhood $\pi $-base (answering a question of Arhangel’skii);   (3)   $X$ is hereditarily paracompact iff $X$ has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal spaces.},
author = {Williams, Scott W., Zhou, Hao Xuan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {monotonically normal; compactness; linear ordered spaces; monotonically normal space; orderable space; compactness},
language = {eng},
number = {1},
pages = {207-217},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Order-like structure of monotonically normal spaces},
url = {http://eudml.org/doc/248276},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Williams, Scott W.
AU - Zhou, Hao Xuan
TI - Order-like structure of monotonically normal spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 207
EP - 217
AB - For a compact monotonically normal space X we prove:   (1)   $X$ has a dense set of points with a well-ordered neighborhood base (and so $X$ is co-absolute with a compact orderable space);   (2)   each point of $X$ has a well-ordered neighborhood $\pi $-base (answering a question of Arhangel’skii);   (3)   $X$ is hereditarily paracompact iff $X$ has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal spaces.
LA - eng
KW - monotonically normal; compactness; linear ordered spaces; monotonically normal space; orderable space; compactness
UR - http://eudml.org/doc/248276
ER -

References

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  16. Rudin M.E., Compact monotonically normal spaces, invited lecture, 8th Prague Topological Symposium, August, 1996. Zbl0983.54021
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  20. Williams S.W., Zhou H., Strong versions of normality, Proceedings of the New York Conference on Topology and its Applications. Zbl0797.54011

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