Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On sums of Darboux and nowhere constant continuous functions
HTML articles powered by AMS MathViewer

by Krzysztof Ciesielski and Janusz Pawlikowski PDF
Proc. Amer. Math. Soc. 130 (2002), 2007-2013 Request permission

Abstract:

We show that the property

  • [(P)] for every Darboux function $g\colon {\mathbb R}\to \mathbb {R}$ there exists a continuous nowhere constant function $f\colon {\mathbb R}\to \mathbb {R}$ such that $f+g$ is Darboux

  • follows from the following two propositions:

  • [(A)] for every subset $S$ of $\mathbb {R}$ of cardinality $\mathfrak {c}$ there exists a uniformly continuous function $f\colon \mathbb {R}\to [0,1]$ such that $f[S]=[0,1]$,

  • [(B)] for an arbitrary function $h\colon \mathbb {R}\to \mathbb {R}$ whose image $h[\mathbb {R}]$ contains a non-trivial interval there exists an $A\subset \mathbb {R}$ of cardinality $\mathfrak {c}$ such that the restriction $h\restriction A$ of $h$ to $A$ is uniformly continuous,

  • which hold in the iterated perfect set model.

    References
    Similar Articles
    • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 26A15, 03E35
    • Retrieve articles in all journals with MSC (1991): 26A15, 03E35
    Additional Information
    • Krzysztof Ciesielski
    • Affiliation: Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310
    • Email: K_Cies@math.wvu.edu
    • Janusz Pawlikowski
    • Affiliation: Department of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland – and – Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310
    • Email: pawlikow@math.uni.wroc.pl
    • Received by editor(s): November 13, 2000
    • Received by editor(s) in revised form: January 24, 2001
    • Published electronically: December 27, 2001
    • Additional Notes: The work of the second author was partially supported by KBN Grant 2 P03A 031 14.
    • Communicated by: Alan Dow
    • © Copyright 2001 American Mathematical Society
    • Journal: Proc. Amer. Math. Soc. 130 (2002), 2007-2013
    • MSC (1991): Primary 26A15; Secondary 03E35
    • DOI: https://doi.org/10.1090/S0002-9939-01-06254-2
    • MathSciNet review: 1896035