Higher separation axioms in L-topologically generated I(L)-topological spaces

Authors:
Tomasz Kubiak;Iraide Mardones-Pérez
Affiliations:
Wydzial Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, 60-769 Poznan, Poland;Matematika Saila, Zientzi Fakultatea, Euskal Herriko Unibertsitatea, 644 P.K., Bilbao 48080, Spain
Venue:
Fuzzy Sets and Systems - Mathematics
Year:
2002

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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 ΩL(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.