On the existence of characteristic functions in bornological bispaces

Let ((S, 1, 2), B) be a bornological bispace, where 1 and 2 are collections of subsets of a set S such that (S, 1) and (S, 2) are spaces alongside a bornology B. This paper extends boundedness concepts across bispaces.A property involving a (1, 2)-characteristic function is introduced.It is shown that the existence of a (1, 2)-characteristic function requires S to be weakly locally bounded, B to be 1-open and 2-closed, and to have a countable base.