On weakly \(\alpha\)-\(\mathcal{I}\)-open sets and a new decomposition of continuity via ideals
type: Item
instance of: scholarly article
title: On weakly \(\alpha\)-\(\mathcal{I}\)-open sets and a new decomposition of continuity via ideals
zbMATH Open document ID: 1212.54042
author: J. Martínez
published in: Southeast Asian Bulletin of Mathematics
publication date: 2010-07-08T00:00:00Z
review text: The authors introduce the concepts of weakly \(\alpha\)-\(\mathcal{I}\)-open and weakly \(\alpha\)-\(\mathcal{I}\)-closed sets in an ideal topological space \( (X,\tau,\mathcal{I})\); some characterization theorems are studied and several examples are provided. In a special type of ideal topological spaces -- called Hayashi-Samuels spaces -- it is shown that the collection of weakly \(\alpha\)-\(\mathcal{I}\)-open sets forms a supratopology. Finally, with the help of \(\alpha\)-\(\mathcal{I}\)-open sets, the authors introduce weakly \(\alpha\)-\(\mathcal{I}\)-continuous functions and study characterization theorems for such functions; this study leads to a new decomposition theorem of continuity.
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 5732106
zbMATH Keywords: topological ideal
zbMATH Keywords: weakly \(\alpha\)-\(\mathcal{I}\)-open sets
zbMATH Keywords: weakly \(\alpha\)-\(\mathcal{I}\)-continuous functions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5732106