Document Type
Article
Department/Program
Mathematics
Journal Title
Topology and Its Applications
Pub Date
2010
Volume
157
Issue
2
First Page
456
Abstract
We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO) spaces. We show, for example, that a generalized ordered space with a sigma-closed-discrete dense subset is metrizable if and only if it is monotonically (countably) metacompact, that a monotonically (countably) metacompact GO-space is hereditarily paracompact. and that a locally countably compact GO-space is metrizable if and only if it is monotonically (countably) metacompact. We give an example of a non-metrizable LOTS that is monotonically metacompact, thereby answering a question posed by S.G. Popvassilev. We also give consistent examples showing that if there is a Souslin line, then there is one Souslin line that is monotonically countable metacompact, and another Souslin line that is not monotonically countably metacompact. (C) 2009 Elsevier B.V. All rights reserved.
Recommended Citation
Lutzer, David J.; Bennett, Harold R.; and Hart, Klaas Pieter, A note on monotonically metacompact spaces (2010). Topology and Its Applications, 157(2), 456-465.
10.1016/j.topol.2009.10.004
DOI
10.1016/j.topol.2009.10.004
