In 1995, J.Dontchev has defined and studied the notions of gsp-open sets, gsp-closed sets,gsp-continuous functions and gsp-irresolute functions in topological spaces. In the literature, many topologists have been utilized and defined various concepts using these gsp-closed sets in topology. Quite recently, Navalagi et al have utilized these gsp-closed sets and gsp-continuity to define and study the concepts of gsp-separation axioms, gsp-Hausdorff spaces, allied gsp-regularity axioms and allied gsp-normality axioms in topology. In this paper, we define and study the notions of allied - gsp-continuity, gsp-openness, gsp-closedness, totally – gsp- continuous functions and gsp-compactness in topology.