Bulletin of the Belgian Mathematical Society - Simon Stevin

Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions

Krzysztof Płotka

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We prove the existence of an additive semigroup of cardinality $2^\mathfrak c$ contained in the intersection of the classes of Hamel functions ($\rm HF$) and Sierpiński-Zygmund functions ($\rm SZ$). In addition, we show that under certain set-theoretic assumptions the lineability of the class of Sierpiński-Zygmund functions ($\rm SZ$) is equal to the lineability of the class of almost continuous Sierpiński-Zygmund functions ($\rm AC\cap\rm SZ$).

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 3 (2015), 447-454.

First available in Project Euclid: 16 September 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15A03: Vector spaces, linear dependence, rank
Secondary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 03E75: Applications of set theory

lineability Hamel functions Sierpiński-Zygmund functions


Płotka, Krzysztof. Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 3, 447--454. doi:10.36045/bbms/1442364591. https://projecteuclid.org/euclid.bbms/1442364591

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