On G-compactness of topological groups with operations

Abstract

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.