Cones,semicontinuous functions,and continuous lattices |
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Authors: | John A Tiller |
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Institution: | (1) Department of Mathematics and Computer Science, Brandon University, Brandon, Manitoba, Canada |
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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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Keywords: | 06B30 |
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