Concerning a characterization of continuity
type: Item
instance of: scholarly article
title: Concerning a characterization of continuity
zbMATH Open document ID: 0879.26011
published in: Real Analysis Exchange
publication date: 1997-12-10T00:00:00Z
review text: The author shows that a real-valued function \(f\) on a \(T_3\) locally connected Baire space is continuous if and only if (1) \(f\) is a Darboux function, (2) \(f\) is almost continuous in the sense of Husain, and (3) \(f\) is not of Cesàro type. This improves a characterization of continuity given by J. Smítal and E. Stanova. Moreover, it is proved that for a function \(f\), the following three conditions are not redundant: (1) \(f\) is extendable, (2) \(f\) is almost continuous in the sense of Husain, (3) \(f\) is not of Cesàro type.
reviewed by: Václav Kelar
Mathematics Subject Classification ID: 26A15
zbMATH DE Number: 1095914
zbMATH Keywords: extendable function
zbMATH Keywords: connectivity function
zbMATH Keywords: almost continuity
author: Richard G. Gibson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1095914