A measure of non-compactness on T3½ spaces based on Arzelà-Ascoli type theorem.

The purpose of this paper is to generalize the measure of non-compactness for the space of continuous functions over the T3½ space. Motivated by the generalized Arzelà-Ascoli theorem for Tichonoff space T via Wallman compactifiaction Wall(T), we constuct a measure of non-compactness for the space Cb(T). We also study some of the properties of this object and give another version of Darbotype theorem, suitable for this particular case. [ABSTRACT FROM AUTHOR]