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On almost sober spaces.

On almost sober spaces.

Authors :
Shan, Qidong
Bao, Meng
Wen, Xinpeng
Xu, Xiaoquan
Source :
Topology & Its Applications. Jan2022, Vol. 305, pN.PAG-N.PAG. 1p.
Publication Year :
2022

Abstract

• The category of all almost sober spaces is not reflective in the category of all T 0 spaces. • Almost sober spaces are closed under retracts and products. • The equalizer of a pair of continuous mappings from an almost sober space to a T 0 space is not almost sober in general. • The function space of almost sober spaces equipped with the topology of pointwise convergence is not almost sober in general. • Smyth power space of an almost sober space may not be almost sober. In this paper, we mainly investigate some basic properties of almost sober spaces. For the category ASob of all almost sober spaces with continuous mappings, it is proved that the ASob -reflection of Johnstone space Σ J does not exist and hence ASob is not reflective in the category Top 0 of all T 0 spaces with continuous mappings. It is shown that some properties which are similar to that of sober spaces hold and others do not hold. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
*FUNCTION spaces
*TOPOLOGY

Details

Language :
English
ISSN :
01668641
Volume :
305
Database :
Academic Search Index
Journal :
Topology & Its Applications
Publication Type :
Academic Journal
Accession number :
153708638
Full Text :
https://doi.org/10.1016/j.topol.2021.107896