Regular \(L\)-fuzzy topological spaces and their topological modifications
type: Item
instance of: scholarly article
title: Regular \(L\)-fuzzy topological spaces and their topological modifications
zbMATH Open document ID: 0951.54009
DOI: 10.1155/S0161171200002507
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-09-19T00:00:00Z
full work available at URL: https://eudml.org/doc/48585
review text: Let \(L\) be a continuous lattice with its Scott topology. There is a functor \(\omega_L\) from the category \textbf{Top} of topological spaces to the category \(L\)-\textbf{Top} of \(L\)-topological spaces. \(\omega_L\) sends every topological space \((X,{\mathcal T})\) to \((X,\omega_L({\mathcal T}))\), where \(\omega_L ({\mathcal T})\) denotes the collection of all continuous functions from \(X\) to \(L\). Conversely, there is also a functor \(\iota_L\) from \(L\)-\textbf{Top} to \textbf{Top}, \(\iota_L\) sends every \(L\)-topological space \((X,\Delta)\) to \((X,\iota_L (\Delta))\), where \(\iota_L(\Delta)\) is the coarsest topology on \(X\) making all \(\lambda \in \Delta\) continuous. In this paper it is showed that both of the functors \(\omega_L\) and \(\iota_L\) preserve regularity. Precisely, if \((X,{\mathcal T})\) is regular then \((X,\omega_L ({\mathcal T}))\) is \(L\)-regular (i.e., regular in the Hutton-Reilly sense); if \((X,\Delta)\) is \(L\)-regular then \((X,\iota_L (\Delta))\) is regular. Moreover, the relationship of \(L\)-regular spaces to \(H\)-Lindelöf spaces and \(L\)-normal spaces is discussed.
reviewed by: Dexue Zhang
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1496729
zbMATH Keywords: \(L\)-regularity
zbMATH Keywords: Lowen functors
zbMATH Keywords: \(L\)-regular spaces
author: Tomasz Kubiak
author: María Angeles de Prada Vicente
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1496729