Decomposing symmetrically continuous

and Sierpinski-Zygmund functions

into continuous functions

Author:
Krzysztof Ciesielski

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3615-3622

MSC (1991):
Primary 26A15; Secondary 03E35

DOI:
https://doi.org/10.1090/S0002-9939-99-04955-2

Published electronically:
May 13, 1999

MathSciNet review:
1618725

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we will investigate the smallest cardinal number such that for any symmetrically continuous function there is a partition of such that every restriction is continuous. The similar numbers for the classes of Sierpinski-Zygmund functions and all functions from to are also investigated and it is proved that all these numbers are equal. We also show that and that it is consistent with ZFC that each of these inequalities is strict.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-99-04955-2

Keywords:
Decomposition number,
symmetrically continuous functions,
Sierpi\'nski-Zygmund functions

Received by editor(s):
November 23, 1997

Received by editor(s) in revised form:
February 18, 1998

Published electronically:
May 13, 1999

Additional Notes:
The author was partially supported by NATO Collaborative Research Grant CRG 950347 and 1996/97 West Virginia University Senate Research Grant.

Communicated by:
Alan Dow

Article copyright:
© Copyright 1999
American Mathematical Society