Real Analysis Exchange

Interpolation of sequences.

Raúl Naulin and Carlos Uzcátegui

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Abstract

We present a generalization of the following result of Y. Benyamini. There is a continuous function $f: \mathbb{R} \to \mathbb{R}$ such that for each (/$x_n)_{n \in \mathbb{Z}}\in [0,1]^\mathbb{Z}$, there is $t \in \mathbb{R}$ such that $x_n=f(t+n)$ for all $n\in \mathbb{Z}$.

Article information

Source
Real Anal. Exchange, Volume 31, Number 2 (2005), 519-523.

Dates
First available in Project Euclid: 10 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184104043

Mathematical Reviews number (MathSciNet)
MR2265792

Zentralblatt MATH identifier
1117.54043

Subjects
Primary: 54E45: Compact (locally compact) metric spaces
Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]

Keywords
interpolation of sequences universal surjectivity of the Cantor set

Citation

Naulin, Raúl; Uzcátegui, Carlos. Interpolation of sequences. Real Anal. Exchange 31 (2005), no. 2, 519--523. https://projecteuclid.org/euclid.rae/1184104043


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References

  • Yoav Benyamini, Applications of the Universal Surjectivity of the Cantor set, American Matemathical Monthly, 105(9) (1998), 832–839.
  • R. Engelking, General Topology, PWN, Warszawa, 1977.
  • A. S. Kechris, Classical descriptive set theory, Springer-Verlag, 1994.
  • Y. N. Moschovakis, Descriptive set theory, North Holland, Amsterdam, 1980.