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The paper develops a novel analysis of mutual interactions between topologyand soft topology. It is known that each soft topology produces a system ofcrisp (parameterized) topologies. The other way round is also possible. Namely,one can generate a soft topology from a system of crisp topologies. Differentmethods of producing soft topologies are discussed by implementing twoformulas. Then, the relationships between the resulting soft topologies areobtained. With the help of an example, it is demonstrated that one formula ismore constructible than the other. Now, it is reasonable to ask which(topological) properties of a soft topology can be transferred to the set ofcrisp topologies or the opposite. To address this question, we consider thestandard separation axioms and show how well these axioms can be preserved whenmoving from a system of crisp topologies to the soft topology generated by itand contrariwise. Additionally, our findings extend and disprove some resultsfrom the literature.

Methods of generating soft topologies and soft separation axioms