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arXiv · 1812.10618

A measure of non-compactness on $T_{3\frac 1 2 }$ spaces based on Arzel\`a-Ascoli type theorem

Filip Turoboś
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Abstract

The purpose of this paper is to generalize the measure of non-compactness for the space of continuous functions over the $T_{3 \frac{1}{2}}$ space. Motivated by the generalized Arzel\`a-Ascoli theorem for Tichonoff space $T$ via Wallman compactifiaction $\operatorname{Wall}(T)$, we constuct a measure of non-compactness for the space $C^b(T)$. We also study some of the properties of this object and give another version of Darbo-type theorem, suitable for this particular case.

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BibTeXRIS

Filip Turoboś. 2018-12-27. A measure of non-compactness on $T_{3\frac 1 2 }$ spaces based on Arzel\`a-Ascoli type theorem. https://doi.org/10.2989/16073606.2019.1654553

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