Cardinal invariants concerning

bounded families of extendable

and almost continuous functions

Authors:
Krzysztof Ciesielski and Aleksander Maliszewski

Journal:
Proc. Amer. Math. Soc. **126** (1998), 471-479

MSC (1991):
Primary 26A21; Secondary 54C08

DOI:
https://doi.org/10.1090/S0002-9939-98-04098-2

MathSciNet review:
1422855

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we introduce and examine a cardinal invariant closely connected to the addition of bounded functions from to . It is analogous to the invariant 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.

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Additional Information

**Krzysztof Ciesielski**

Affiliation:
Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506–6310

Email:
kcies@wvnvms.wvnet.edu

**Aleksander Maliszewski**

Affiliation:
Department of Mathematics, Pedagogical University, Arciszewskiego 22, 76–200 Słupsk, Poland

Email:
wspb05@pltumk11.bitnet

DOI:
https://doi.org/10.1090/S0002-9939-98-04098-2

Keywords:
Peripheral continuity,
almost continuity,
connectivity,
extendability

Received by editor(s):
March 28, 1996

Received by editor(s) in revised form:
August 11, 1996

Additional Notes:
This work was partially supported by NSF Cooperative Research Grant INT-9600548

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1998
American Mathematical Society