A classification of CO spaces which are continuous images of compact ordered spaces
| dc.creator | Bonnet, Robert | |
| dc.creator | Rubin, Matatyahu | |
| dc.date | 2007-06-12 | |
| dc.date.accessioned | 2026-07-07T08:05:16Z | |
| dc.date.available | 2026-07-07T08:05:16Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0706.1686 | |
| dc.identifier | http://arxiv.org/abs/0706.1686 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130228 | |
| dc.subject | General Topology | |
| dc.subject | 06E05; 54G12; 06A05 | |
| dc.title | A classification of CO spaces which are continuous images of compact ordered spaces | |
| dc.type | text |