Cardinal invariants concerning bounded families of extendable and almost continuous functions


Krzysztof Ciesielski & Aleksander Maliszewski

Proc. Amer. Math. Soc. 126(2) (1998), 471-479.

In this paper we introduce and examine a cardinal invariant Ab closely connected to the addition of bounded functions from R to R. It is analogous to the invariant A defined earlier for arbitrary functions by T. Natkaniec. In particular, it is proved that each bounded function can be written as the sum of two bounded almost continuous functions, and an example is given that there is a bounded function which cannot be expressed as the sum of two bounded extendable functions.

LaTeX 2e source file. Requires amssymb.sty, amsmath.sty and amsthm.sty

DVI and Postscript files are available at the Topology Atlas preprints side.

The following works have cited this article

Journal Articles

H. Rosen, Every real function is the sum of two extendable connectivity functions, Real Anal. Exchange 21(1) (1996), 299--303.

K. Ciesielski, Set Theoretic Real Analysis, J. Appl. Anal. 3(2) (1997), 143-190. MR 99k:03038

R. G. Gibson and T. Natkaniec, Darboux like functions, Real Anal. Exchange 22(2) (1997), 492--533.

A. Maliszewski, Darboux Property and Quasi-continuity: a uniform approach, Pedagogical University, Slupsk, Poland, 1996.

Last modified January, 2014.