Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

Soft omega-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft omega-regularity as a weaker form of both soft regularity and soft omega-local indiscreetness is defined and investigated. Additionally, soft omega-T-2 as a new soft topological property that lies strictly between soft T-2 and soft T-1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft omega-locally indiscreetness (resp. soft omega-regularity) and soft locally indiscreetness (resp. soft omega-regularity). Additionally, it is proved that the induced topological spaces of a soft omega-locally indiscrete (resp. soft omega-regular, soft omega-T-2) soft topological space are (resp. omega-regular, omega-T-2) topological spaces. Additionally, it is proved that the generated soft topological space of a family of omega-locally indiscrete (resp. omega-regular, omega-T-2) topological spaces is soft omega-locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft omega-regular and soft omega-T-2 soft topological spaces are obtained. Moreover, it is proved that soft omega-regular and soft omega-T-2 are hereditarily under soft subspaces.