Separating sets in bitopological spaces by ????-LSC and ℒ-USC functions

Abstract

In this paper we characterize the pairs ⟨A₀, A₁⟩ and ⟨A⁻, A⁺⟩ of disjoint subsets of bitopological space (X, ????, ℒ) which can be separated by the function f : X → ℝ simultaneously lower semicontinuous in the topology ???? and upper semicontinuous in the topology ℒ.