Abstract
The main result of this paper is a theorem about inserting a pair of semicontinuous L-real-valued functions which extends the insertion theorem of Kubiak [Comment. Math. Univ. Carolinae 34 (1993) 357–362] from L={0,1} to an arbitrary meet-continuous lattice L (endowed with an order-reversing involution). With this result it is shown that the normality-type separation axioms in TOP (L) are preserved by the functor which takes an L-topological space X to the I(L) -topological space Ω L(X) obtained by providing the set X with the I(L) -topology consisting of all lower semicontinuous functions from X to I(L) . The same is proved for the case of the regularity axiom.
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