Abstract

The concept of a quasi-king space is introduced, 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.

Keywords: Vietoris topology; separately continuous weak selection; coarser topology; weakly orderable space; quasi-king space; pseudocompact space.

MSC: 54B20, 54C65, 54D30, 54F05

Pages:  350$-$363     

Volume  70 ,  Issue  4 ,  2018