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On uniformly continuous maps between function spaces

Volume 246 / 2019

Rafał Górak, Mikołaj Krupski, Witold Marciszewski Fundamenta Mathematicae 246 (2019), 257-274 MSC: Primary 54C35; Secondary 54E15. DOI: 10.4064/fm647-10-2018 Published online: 17 May 2019

Abstract

We develop a technique of constructing uniformly continuous maps between function spaces endowed with the pointwise topology. We prove that if X is compact metrizable and strongly countable-dimensional, then there exists a uniformly continuous surjection from C_p([0,1]) onto C_p(X). We provide a partial converse. We also show that, for every infinite Polish zero-dimensional space X, the spaces C_p(X) and C_p(X) \times C_p(X) are uniformly homeomorphic.

Authors

  • Rafał GórakTechnical University of Warsaw
    Pl. Politechniki 1
    00-661 Warszawa, Poland
    e-mail
  • Mikołaj KrupskiInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    and
    Department of Mathematics
    University of Pittsburgh
    Pittsburgh, PA 15260, U.S.A.
    e-mail
  • Witold MarciszewskiInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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