An example of an additive almost continuous Sierpiński-Zygmund function. (English) Zbl 1060.26004

Natkaniec, Tomasz; Rosen, Harvey

Real Anal. Exch. 30(2004-2005), No. 1, 261-266 (2005).

Summary: Assuming that the union of fewer than \({\mathfrak c}\)-many meager sets does not cover the real line, we construct an example of an additive almost continuous Sierpiński-Zygmund function which has a perfect road at each point but which does not have the Cantor intermediate value property.

MSC:

26A15	Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
03E50	Continuum hypothesis and Martin’s axiom

Keywords:

meager sets; almost continuity; additive function; Sierpiński-Zygmund function; perfect road; Cantor intermediate value property