On uniformly continuous maps between function spaces

Rafal Gorak; Mikolaj Krupski; Witold Marciszewski

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arXiv · 1710.10510

On uniformly continuous maps between function spaces

Rafal Gorak·Mikolaj Krupski·Witold Marciszewski

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Abstract

In this paper we develop a technique of constructing uni- formly continuous maps between function spaces Cp(X) endowed with the pointwise topology. We prove that if a space X is compact metrizable and strongly countable-dimensional, then there exists a uniformly contin- uous surjection from Cp([0,1]) onto Cp(X). We provide a partial result concerning the reverse implication. We also show that, for every infinite Polish zero-dimensional space X, the spaces Cp(X) and Cp(X) x Cp(X) are uniformly homeomorphic. This partially answers two questions posed by Krupski and Marciszewski.

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BibTeX RIS

Rafal Gorak, Mikolaj Krupski, Witold Marciszewski. 2017-10-28. On uniformly continuous maps between function spaces. https://arxiv.org/abs/1710.10510

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