Darboux like functions
type: Item
instance of: scholarly article
title: Darboux like functions
zbMATH Open document ID: 0942.26004
author: Richard G. Gibson
author: Tomasz Natkaniec
published in: Real Analysis Exchange
publication date: 2000-05-22T00:00:00Z
review text: The article contains a survey of research that has been done concerning the intermediate value property of real functions of a real variable and related properties. The following classes of functions are discussed: Darboux functions, peripherally continuous functions, connectivity functions, almost continuous functions in the sense of Stallings, extendable functions, functions with a perfect road, functions having the (weak, strong) Cantor intermediate value property, functions with property~\(B\). Functions from these classes are called briefly Darboux like functions. The survey includes Darboux like functions in the first class of Baire, Borel, Lebesgue and Marczewski measurability of Darboux like functions, Darboux like properties of Sierpiński-Zygmund functions, additive functions and quasi-continuous functions, characterizations of Darboux like functions, Darboux like functions of several variables, algebraic operations. Some open questions are posed.
reviewed by: Václav Kelar
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 1450282
zbMATH Keywords: Darboux functions
zbMATH Keywords: extendable functions
zbMATH Keywords: connectivity functions
zbMATH Keywords: functions with perfect road
zbMATH Keywords: peripherally continuous functions
zbMATH Keywords: DIVP-functions
zbMATH Keywords: CIVP-functions
zbMATH Keywords: SCIVP-functions
zbMATH Keywords: WCIVP-functions
zbMATH Keywords: Sierpiński-Zygmund functions
zbMATH Keywords: property B
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1450282