Abstract
The purpose of this paper is to introduce a notion which is a generalization of convex sets and to use this notion to construct continuous lattices which are shown to be related to lattices of lower-semicontinuous functions. The end results of this development is a characterization of lattices of lower-semicontinuous functions in terms of a class of continuous lattices introduced in this paper (see Theorem 8). Then material is introduced which leads to a complementary result in Theorem 11 which characterizes the continuous lattices that can be lattices of lower-semicontinuous functions.
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References
GierzG., K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott (1980) A Compendium of Continuous Lattices Springer, New York.
Nachbin, L. (1986) Topology and Order, Van Nostrand.
TillerJ. (1981) Augmented compact spaces and continuous lattices, Houston J. Math. 7, 441–453.
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Communicated by K. Keimel
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Tiller, J.A. Cones, semicontinuous functions, and continuous lattices. Order 3, 299–306 (1986). https://doi.org/10.1007/BF00400293
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DOI: https://doi.org/10.1007/BF00400293