A classification of CO spaces which are continuous images of compact ordered spaces

Details A classification of CO spaces which are continuous images of compact ordered spaces A classification of CO spaces which are continuous images of compact ordered spaces

2007-06-12

arxiv.org/abs/0706.1686v1

Mathematics

General Topology

Scientific paper

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.

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