Lattice-valued semiuniform convergence spaces
type: Item
instance of: scholarly article
title: Lattice-valued semiuniform convergence spaces
zbMATH Open document ID: 1256.54022
author: Jin-Ming Fang
published in: Fuzzy Sets and Systems
publication date: 2012-11-21T00:00:00Z
review text: The author studies two extensions of the category of semiuniform convergence spaces, namely the categories \(SL\)-\textbf{SUConv} of stratified \(L\)-semiuniform convergence spaces and \(SL\)-\textbf{OSUConv} of stratified \(L\)-ordered semiuniform convergence spaces, where \(L\) denotes an arbitrary complete Heyting algebra. It is shown that (i) \(SL\)-\textbf{SUConv} is topological; (ii) \(SL\)-\textbf{OSUConv} is a bireflective full subcategory of \(SL\)-\textbf{SUConv}, and hence it is topological; (iii) both categories are Cartesian-closed; (iv) \(SL\)-\textbf{SUConv} is extensional; (v) both categories are closed under the formation of products of quotient mappings.
reviewed by: Javier Gutiérrez García
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 6109294
zbMATH Keywords: topology
zbMATH Keywords: \(L\)-filter
zbMATH Keywords: \(L\)-semiuniform convergence space
zbMATH Keywords: \(L\)-ordered semiuniform convergence space
zbMATH Keywords: topological category
zbMATH Keywords: Cartesian-closedness
zbMATH Keywords: extensionality
zbMATH Keywords: product of quotient mappings
MaRDI profile type: Publication
full work available at URL: j.fss.2011.10.017
OpenAlex ID: W2001708978
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DOI: 10.1016/J.FSS.2011.10.017
description: scientific article; zbMATH DE number 6109294