Compact-bounded topological groups

We will study two subclasses of the class of feebly compact spaces in the class of (para)topological groups, the compact-bounded and weakly compact-bounded spaces, both introduced by J. Angoa, Y. F. Ortiz-Castillo and A. Tamariz-Mascarúa in [4]. Also, we will study the $r$-weakly compact-bounded subsets of a topological space $X$.