Real Analysis Exchange

An example of an additive almost continuous Sierpiński-Zygmund Function

Tomasz Natkaniec and Harvey Rosen

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Assuming that the union of fewer than continuumly many meager sets does not cover the real line, we construct an example of an additive almost continuous Sierpi{\'n}ski-Zygmund function which has a perfect road at each point but which does not have the Cantor intermediate value property.

Article information

Real Anal. Exchange, Volume 30, Number 1 (2004), 261-266.

First available in Project Euclid: 27 July 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 03E50: Continuum hypothesis and Martin's axiom [See also 03E57]

almost continuous additive function Sierpi{\'n}ski-Zygmund function perfect road Cantor Intermediate Value Property


Natkaniec, Tomasz; Rosen, Harvey. An example of an additive almost continuous Sierpiński-Zygmund Function. Real Anal. Exchange 30 (2004), no. 1, 261--266.

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