Darboux-like functions within the classes of Baire one, Baire two, and additive functions
type: Item
instance of: scholarly article
title: Darboux-like functions within the classes of Baire one, Baire two, and additive functions
zbMATH Open document ID: 0951.26003
DOI: 10.1016/S0166-8641(98)00169-2
published in: Topology and its Applications
publication date: 2000-09-04T00:00:00Z
review text: The authors consider relations between Darboux-like functions [see \textit{R.~G.~Gibson, T.~Natkaniec}, Real Anal. Exch. 22, No.~2, 492-533 (1996; Zbl 0942.26004)] within the classes of Baire one, Baire two, Borel and additive functions from \({\mathbb{R}}^n \to {\mathbb{R}}\). Main results: (1) There exists an almost continuous, Baire class two function \(f\colon {\mathbb{R}}\to {\mathbb{R}}\) which is not extendable. (2) There exists an additive extendable function \(f\colon {\mathbb{R}}\to {\mathbb{R}}\) which is not continuous. (3) For \(n>1\) every additive, almost continuous Darboux function \(f\colon \mathbb{R}^n\to \mathbb{R}\) is continuous.
reviewed by: Tomasz Natkaniec
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 1455643
zbMATH Keywords: extendable function
zbMATH Keywords: almost continuous function
zbMATH Keywords: additive function
zbMATH Keywords: Baire class one
zbMATH Keywords: Baire class two
zbMATH Keywords: Darboux function
author: Krzysztof Chris Ciesielski
author: Jan Jastrzȩbski
MaRDI profile type: Publication
Wikidata QID: Q126819540
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description: scientific article; zbMATH DE number 1455643