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Separating sets in bitopological spaces by P-LSC and L-USC 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