Quasicontinuous spaces

Jing Lu; Bin Zhao; Kaiyun Wang; Dong Sheng Zhao

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 4, page 513-526
  • ISSN: 0010-2628

Abstract

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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 , τ ) is a quasicontinuous space if and only if S I ( X ) is locally hypercompact if and only if ( τ S I , ⊆ ) is a hypercontinuous lattice; (2) a T 0 space X is an S I -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.

How to cite

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Lu, Jing, et al. "Quasicontinuous spaces." Commentationes Mathematicae Universitatis Carolinae 62 63.4 (2022): 513-526. <http://eudml.org/doc/299034>.

@article{Lu2022,
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.},
author = {Lu, Jing, Zhao, Bin, Wang, Kaiyun, Zhao, Dong Sheng},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasicontinuous space; hypercontinuous lattice; $SI$-continuous space; locally hypercompact space; meet continuous space},
language = {eng},
number = {4},
pages = {513-526},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quasicontinuous spaces},
url = {http://eudml.org/doc/299034},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Lu, Jing
AU - Zhao, Bin
AU - Wang, Kaiyun
AU - Zhao, Dong Sheng
TI - Quasicontinuous spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 4
SP - 513
EP - 526
AB - 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.
LA - eng
KW - quasicontinuous space; hypercontinuous lattice; $SI$-continuous space; locally hypercompact space; meet continuous space
UR - http://eudml.org/doc/299034
ER -

References

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