Geodesic
Quasicontinuous spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 4, pp. 513-526.

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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.
DOI : 10.14712/1213-7243.2023.005
Classification : 06B30, 06B35, 54D10
Keywords: quasicontinuous space; hypercontinuous lattice; $SI$-continuous space; locally hypercompact space; meet continuous space 
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Lu, Jing; Zhao, Bin; Wang, Kaiyun; Zhao, Dongsheng. Quasicontinuous spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 4, pp. 513-526. doi : 10.14712/1213-7243.2023.005. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.005/

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