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- W2015799993 abstract "In this paper, we shall generalize the Hahn-Dieudonné-Tong Insertion Theorem, a classical result on semicontinuous functions, to the case that the ranges are a certain kind of lattices L . We consider the family of all lattice-valued (lower) semicontinuous mappings as a topology, and then solve this problem via reducing it to a problem on a certain kind of separation property. Therefore, as a by-product, the following theorem is obtained for a suitable range L : An induced space is normal if and only if the underlying space is normal. The relative counterexamples show that the limitation for L is necessary. These results and counterexamples point out that normality of induced spaces and the existence of latticed-valued inserting mappings close relates to the internal characterization of the range L . The previous proofs of the classical insertion theorem are analytic and skillful; compared with them, the present method determining mappings via the stratifications is very natural and conceptual. The success of the method is based on the study in depth on the topological relations among the stratifications. We may hope that the method, which determines the mapping via inductively getting its stratifications, will be further applied in other aspects." @default.
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- W2015799993 date "1992-06-01" @default.
- W2015799993 modified "2023-09-26" @default.
- W2015799993 title "Lattice-valued Hahn-Dieudonné-Tong insertion theorem and stratification structure" @default.
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- W2015799993 doi "https://doi.org/10.1016/0166-8641(92)90003-i" @default.
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