Jing Lu, Bin Zhao, Kaiyun Wang, Dongsheng Zhao
Quasicontinuous spaces

Comment.Math.Univ.Carolin. 63,4 (2022) 513-526.

Abstract: We lift the notion of quasicontinuous posets to the topology context, called quasicontinuous spaces, and further study such spaces. The main results are: (1) A T_{0} space (X,\tau) is a quasicontinuous space if and only if SI(X) is locally hypercompact if and only if (\tau_{SI},\subseteq) is a hypercontinuous lattice; (2) a T_{0} space X is an SI-continuous space if and only if X is a meet continuous and quasicontinuous space; (3) if a C-space X is a well-filtered poset under its specialization order, then X is a quasicontinuous space if and only if it is a quasicontinuous domain under the specialization order; (4) there exists an adjunction between the category of quasicontinuous domains and the category of quasicontinuous spaces which are well-filtered posets under their specialization orders.

Keywords: quasicontinuous space; hypercontinuous lattice; SI-continuous space; locally hypercompact space; meet continuous space

DOI: DOI 10.14712/1213-7243.2023.005
AMS Subject Classification: 54D10 06B35 06B30