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Remark on the graph of additive functions

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We give a short proof for the theorem that the graph of additive functions is either connected or totally disconnected.

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  1. Hamel G.: Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: f(x + y) = f(x) + f(y). Math. Ann. 60(3), 459–462 (1905)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hewitt E., Ross K.A.: Abstract Harmonic Analysis, vol. I. Springer, Berlin, New York (1979)

    MATH  Google Scholar 

  3. Jones F.B.: Connected and disconnected plane sets and the functional equation f(x) + f(y) = f(x + y). Bull.Am. Math. Soc. 48, 115–120 (1942)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kelley J.L.: General Topology. Springer, New York,Berlin (1975)

    MATH  Google Scholar 

  5. Kuczma M.: An introduction to the theory of functional equations and inequalities. Birkhäuser Verlag, Basel (2009)

    Book  MATH  Google Scholar 

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Correspondence to László Székelyhidi.

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Dedicated to Prof. Roman Ger on his 70th birthday

The research was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. K111651.

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Székelyhidi, L. Remark on the graph of additive functions. Aequat. Math. 90, 7–9 (2016).

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