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Quasicontinuous spaces
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Type
Article
Citation
Lu, J., Zhao, B., Wang, K., & Zhao, D. (2022). Quasicontinuous spaces. Commentationes Mathematicae Universitatis Carolinae, 63(4), 513-526. https://doi.org/10.14712/1213-7243.2023.005
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.
Publisher
Charles University
Journal
Commentationes Mathematicae Universitatis Carolinae
DOI
10.14712/1213-7243.2023.005
Description
The open access publication is available at: https://doi.org/10.14712/1213-7243.2023.005