Monotone insertion of lattice-valued functions |
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Authors: | I Mardones-Pérez M A de Prada Vicente |
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Institution: | (1) Departamento de Matemáticas, Euskal Herriko Unibertsitatea, Aptdo. 644, 48080 Bilbao, Spain |
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Abstract: | Insertion of lattice-valued functions in a monotone manner is investigated. For L a ⊲-separable completely distributive lattice (i.e. L admits a countable base which is free of supercompact elements), a monotone version of the Katětov-Tong insertion theorem
for L-valued functions is established. We also provide a monotone lattice-valued version of Urysohn’s lemma. Both results yield
new characterizations of monotonically normal spaces. Moreover, extension of lattice-valued functions under additional assumptions
is shown to characterize also monotone normality.
This research was supported by the MEyC and FEDER under grant MTM2006-14925-C02-02/ and by UPV05/101 |
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Keywords: | insertion completely distributive lattice scale Raney relation lower semicontinuous function upper semicontinuous function monotone normality |
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