Normally preordered spaces and utilities
General Topology
2013-06-21 v2
Abstract
In applications it is useful to know whether a topological preordered space is normally preordered. It is proved that every -space equipped with a closed preorder is a normally preordered space. Furthermore, it is proved that second countable regularly preordered spaces are perfectly normally preordered and admit a countable utility representation.
Cite
@article{arxiv.1106.4457,
title = {Normally preordered spaces and utilities},
author = {E. Minguzzi},
journal= {arXiv preprint arXiv:1106.4457},
year = {2013}
}
Comments
17 pages, 1 figure. v2 contains a second proof to the main theorem with respect to the published version. The last section of v1 is not present in v2. It will be included in a different work