Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions
type: Item
instance of: scholarly article
title: Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions
zbMATH Open document ID: 1350.26005
author: Krzysztof Płotka
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2015-11-02T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1442364591
review text: The author focuses on specific classes of real-valued functions of one real variable. In particular classes of extendability (Ext) functions, almost continuous (AC) fuctions, Hamel (HF) functions, and Sierpiński-Zygmund (SZ) functions are considered. It is shown that there exists a large semigroup (of cardinality \(2^{\mathfrak{c}}\), where \(\mathfrak{c}\) stands for the cardinality of the set of real numbers) in the intersection of classes HF\(\,\cap\,\)SZ, Ext\(\,\cap\,\)HF, and AC\(\,\cap\,\)HF\(\,\cap\,\)SZ (under some further additional assumptions from set-theory). It is also shown that the lineability of the classs of SZ functions is equal to the lineability of the class of AC\(\,\cap\,\)SZ functions.
reviewed by: Martin Plešinger
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 03E75
zbMATH DE Number: 6502899
zbMATH Keywords: lineability
zbMATH Keywords: almost continuous functions
zbMATH Keywords: Hamel functions
zbMATH Keywords: Sierpiński-Zygmund functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6502899