One can notice that if X is a Hausdorff space, then limits of convergent sequences in X give us a function denoted by lim from the set of all convergent sequences in X to X. This notion has been extended by Connor and Grosse-Erdmann to an arbitrary linear functional G defined on a subspace of the vector space of real numbers. Following this idea some authors have defined concepts of G-continuity, G-compactness and G-connectedness in topological groups. In this paper we present some results about G-compactness of topological group with operations such as topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras and many others.