Cardinal invariants concerning bounded families of extendable and almost continuous functions
Authors:
Krzysztof Ciesielski and Aleksander Maliszewski
Journal:
Proc. Amer. Math. Soc. 126 (1998), 471479
MSC (1991):
Primary 26A21; Secondary 54C08
MathSciNet review:
1422855
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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:
http://dx.doi.org/10.1090/S0002993998040982
PII:
S 00029939(98)040982
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 INT9600548
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1998 American Mathematical Society
