Separating sets in bitopological spaces by <i>P-LSC</i> and <i>L-USC</i> functions

Abstract

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

Mathematics Subject Classification (2010): Primary 26A21, 54E55; Secondary 26A15, 54C08.

Keywords: Bitopological spaces, upper semicontinuous functions, lower semicontinuous functions, Urysohn's lemma, separating sets