MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Coarser compact topologies
V. Gutev

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.

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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