A classification of CO spaces which are continuous images of compact ordered spaces
General Topology
2007-06-13 v1
Abstract
A compact Hausdorff space X is called a CO space, if every closed subset of X is homeomorphic to an open subset of X. Every successor ordinal with its order topology is a CO space. We find an explicit characterization of the class K of CO spaces which are a continuous image of a Dedkind complete totally ordered set. (The topology of a totally ordered set is taken to be its order topology). We show that every member of K can be described as a finite disjoint sum of very simple spaces. Every summand has either form: (1) mu + 1 + nu^*, where mu and nu are cardinals, and nu^* is the reverse order of nu; or (2) the summand is the 1-point-compactification of a discrete space with cardinality aleph_1.
Keywords
Cite
@article{arxiv.0706.1686,
title = {A classification of CO spaces which are continuous images of compact ordered spaces},
author = {Robert Bonnet and Matatyahu Rubin},
journal= {arXiv preprint arXiv:0706.1686},
year = {2007}
}