Separation Axioms on Bipolar Hypersoft Topological Spaces

Book excerpt: According to its definition, a topological space could be a highly unexpected object. There are spaces (indiscrete space) which have only two open sets: the empty set and the entire space. In a discrete space, on the other hand, each set is open. These two artificial extremes are very rarely seen in actual practice. Most spaces in geometry and analysis fall somewhere between these two types of spaces. Accordingly, the separation axioms allow us to say with confidence whether a topological space contains a sufficient number of open sets to meet our needs. To this end, we use bipolar hypersoft (BHS) sets (one of the efficient tools to deal with ambiguity and vagueness) to define a new kind of separation axioms called BHS e Ti-space (i = 0, 1, 2, 3, 4).