Separating sets by bilaterally quasi-continuous functions

Abstract

In this paper we characterize the pairs (A₀;A₁) and (A^-, A⁺) of disjoint sets which can be separated by a bilaterally quasi-continuous function. Moreover, we characterize when two arbitrary subsets of the real line can be separated by bilaterally dense in themselves semi-open sets.

Mathematics Subject Classification (2010): Primary: 26A21, 54C30; Secondary: 26A15, 54C08.