An innovative collection of openR setsR, specifically αγos-openR setsR are offered by this paper authors and its rudimentary properties utilizing the respective τγos-interiorR and τγos- closureR operatorsR are premeditated in their previous papers. As well, it has been substantiated that the idea of γos-openR setsR besides αγos - openR setsR are autonomous and each γos-openR setR is an αos openR setR, but the contrary need not be exact. The perceptions of αγos Ti spacesR also their properties are familiarized and recognized the connection among these spacesR  by establishing several Theorems, undistinguishable statements, consequences besides corollaries. Another new collection of openR setsR namely α(γos, γ¢os)-openR setsR was introduced and their properties were presented with the corresponding interiorR and closureR operators. Further the idea of α(γos, γ¢os) Ti spacesR were adapted and documented the connection among these spaces by providing several theorems.   The theory of α(γos, γ¢os) Ri spacesR have been familiarized and their descriptions have been premeditated by illustrating τα(γos, γ¢os) -kernel and several statements comprehend to that idea. Also the association amongst these α(γos, γ¢os) Ri spacesR have been formed and evaluated by means of several axioms and opposite affirmations.