On fuzzy sobriety
type: Item
instance of: scholarly article
title: On fuzzy sobriety
zbMATH Open document ID: 0930.54012
DOI: 10.1016/S0020-0255(97)10038-X
author: Arun K. Srivastava
author: Anuruddha S. Khastgir
published in: Information Sciences
publication date: 1999-11-23T00:00:00Z
review text: A \(T_0\) topological space \(X\) is called sober iff every irreducible non-empty closed set of \(X\) is of the form \(\overline x\) for a (unique) \(x\in X\). It is known that the category of sober spaces is the epireflective hull of the Sierpinski space 2 in the category of \(T_0\) spaces. \textit{S. E. Rodabaugh} [Fuzzy Sets Syst. 40, No. 2, 297-345 (1991; Zbl 0733.54003)], \textit{D. Zhang} and \textit{Y. Liu} [ibid. 56, No. 2, 215-227 (1993; Zbl 0787.54011); 76, No. 2, 259-270 (1995; Zbl 0852.54008)] generalized the idea of sobriety to fuzzy topological spaces and stratified fuzzy topological spaces respectively. In this paper the author proved that the category of (stratified) fuzzy sober spaces is the epireflective hull of the (stratified resp.) fuzzy Sierpinski space \((I,\Delta)\) \(((I,\Delta^c))\) in the category of (stratified resp.) \(T_0\) fuzzy spaces, where \(\Delta= \{0,1,id\}\) and \(\Delta^c\) is the stratification of \(\Delta\).
reviewed by: Dexue Zhang
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 1326005
zbMATH Keywords: epireflective hull
zbMATH Keywords: Sierpinski space
zbMATH Keywords: fuzzy sober spaces
MaRDI profile type: Publication
cites work: Epireflections in the category of $T_0$-spaces
cites work: Q4693062
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cites work: Fuzzy topological spaces
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full work available at URL: s0020-0255(97)10038-x
OpenAlex ID: W1996094429
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description: scientific article; zbMATH DE number 1326005