Compactifications and remainders of monotonically normal spaces

Monotonically normal spaces have many strong properties, but poor preservation properties. For example, there are locally compact, monotonically normal spaces whose one-point compactifications are not monotonically normal, and hence have no monotonically normal compactifications. We give two classes...

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Bibliographic Details
Published in:Topology and its applications 2016-11, Vol.213, p.80-91
Main Authors: Junnila, Heikki, Nyikos, Peter
Format: Article
Language:English
Subjects:
[formula omitted]-Compact
Compact
Compactification
Countably compact
Ladder system
Locally compact
Locally connected
Metrizable
Monotonically normal
Pointwise countable type
Strongly paracompact
UNO
Utterly normal
σ-Countably compact
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Summary:Monotonically normal spaces have many strong properties, but poor preservation properties. For example, there are locally compact, monotonically normal spaces whose one-point compactifications are not monotonically normal, and hence have no monotonically normal compactifications. We give two classes of such spaces, and give a pair of necessary conditions for spaces of pointwise countable type to have, respectively, compactifications or remainders that are monotonically normal. We show that a monotonically normal, locally compact space has a monotonically normal compactification if it is either locally connected or countably compact, and show that this latter condition cannot be weakened to “σ-countably compact.”
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2016.08.015