\(\theta\)-regular spaces
type: Item
instance of: scholarly article
title: \(\theta\)-regular spaces
zbMATH Open document ID: 0577.54012
DOI: 10.1155/S0161171285000667
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/45986
review text: Summary: A topological space X is called \(\theta\)-regular if every filterbase in X with a nonempty \(\theta\)-adherence has a nonempty adherence. It is shown that the class of \(\theta\)-regular spaces includes rim-compact spaces and that \(\theta\)-regular H(i) (Hausdorff) spaces are compact (regular). The concept of \(\theta\)-regularity is used to extend a closed graph theorem of \textit{D. A. Rose} [Can. Math. Bull. 21, 477-481 (1978; Zbl 0394.54004)]. It is established that an r-subcontinuous closed graph function into a \(\theta\)-regular space is continuous. Another sufficient condition for continuity of functions due to Rose (loc. cit.) is also extended by introducing the concept of almost weak continuity which is weaker than both weak continuity of Levine and almost continuity of Husain. It is shown that an almost weakly continuous closed graph function into a strongly locally compact space is continuous.
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54D45
zbMATH DE Number: 3923638
zbMATH Keywords: \(\theta \) -regular spaces
zbMATH Keywords: rim-compact spaces
zbMATH Keywords: closed graph theorem
zbMATH Keywords: almost weak continuity
zbMATH Keywords: strongly locally compact space
author: Dragan Janković
MaRDI profile type: Publication
OpenAlex ID: W2081978197
description: scientific article; zbMATH DE number 3923638