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

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.

Categories: math.GN math.FA