On the reflectivity and coreflectivity of \(L\)-fuzzyfying topological spaces in \(L\)-topological spaces.
type: Item
instance of: scholarly article
title: On the reflectivity and coreflectivity of \(L\)-fuzzyfying topological spaces in \(L\)-topological spaces.
zbMATH Open document ID: 1051.54008
author: Dexue Zhang
publication date: 2002-01-01T00:00:00Z
review text: Considering \(L\) as a completely distributive lattice, the author proves that the well-known category TOP of topological spaces can be embedded in the category \(L\)-FYS of \(L\)-fuzzifying topological spaces as a both bireflective and bicoreflective full subcategory, although TOP contains no simultaneously bireflective and bicoreflective full subcategories [\textit{V. Kannan}, Math. Ann. 195, 168--174 (1972; Zbl 0215.09701)]. The author also proves that the category \(L\)-FYS can be embedded in the category \(L\)-TOP of stratified Chang-Gougen topological spaces as a simultaneously bireflective and bicoreflective full subcategory. Various relationships among some other categories are also investigated.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 1757446
zbMATH Keywords: topological category
reviewed by: T. M. G. Ahsanullah
MaRDI profile type: Publication
full work available at URL: s101140100109
OpenAlex ID: W2020566959
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DOI: 10.1007/S101140100109
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1757446