Coarser Compact Topologies
General Topology
2019-02-05 v1
Abstract
It is introduced the concept of a quasi-king space, which is a natural generalisation of a king space. In the realm of suborderable spaces, king spaces are precisely the compact spaces, so are the quasi-king spaces. In contrast, quasi-king spaces are more flexible in handling coarser selection topologies. The main purpose of this paper is to show that a weakly orderable space is quasi-king if and only if all of its coarser selection topologies are compact.
Cite
@article{arxiv.1805.10947,
title = {Coarser Compact Topologies},
author = {Valentin Gutev},
journal= {arXiv preprint arXiv:1805.10947},
year = {2019}
}