Cardinal invariants concerning bounded families of extendable and almost continuous functions
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- by Krzysztof Ciesielski and Aleksander Maliszewski PDF
- Proc. Amer. Math. Soc. 126 (1998), 471-479 Request permission
Abstract:
In this paper we introduce and examine a cardinal invariant $\operatorname {A}_{{b}}$ closely connected to the addition of bounded functions from $\mathbb {R}$ to $\mathbb {R}$. It is analogous to the invariant $\operatorname {A}$ 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.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- 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