Form the series of generalization of the topic of supra topology is the generalization  of separation axioms .  In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces       have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.

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In this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly-regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.