Functional Boundedness of Balleans: Coarse Versions of Compactness

Abstract

We survey some results and pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Special attention is paid to balleans on groups. The boundedness of functions that respect the coarse structure of a ballean could be considered as a coarse counterpart of pseudo-compactness.

Keywords

• coarse structure
• ballean
• group
• real-valued function
• boundedness