# 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

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topWilliams, 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 -

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