A measure of non-compactness on T 3½ spaces based on Arzelà-Ascoli type theorem

Abstract

The purpose of this paper is to generalize the measure of non-compactness for the space of continuous functions over the T _3½ 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 C^b (T). We also study some of the properties of this object and give another version of Darbotype theorem, suitable for this particular case.

Mathematics Subject Classification (2010): 46B50, 47H08, 54D35, 54D80.