A measure of non-compactness on T 3½ 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 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 Cb (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.