Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4657750 | Topology and its Applications | 2016 | 12 Pages |
Abstract
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.”
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Heikki Junnila, Peter Nyikos,