On Hypertopologies |
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Authors: | D V Pai B M Deshpande |
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Institution: | Department of Mathematics , Indian Institute of Technology , Bombay, Powai, Mumbai , 400076 , India |
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Abstract: | In this article a unified approach is presented to hypertopologies on collections of nonempty closed subsets of a Hausdorff uniform space generated by a saturated and separating family of pseudo-metrics. One identifies here a suitable topology on the family of proper, convex and lower semicontinuous functions defined on a Hausdorff locally convex space for which the Young Fenchel transform is bicontinuous. This improves a well known result due to Mosco, Joly and Beer. |
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Keywords: | 54B20 52A07 54C35 49J45 |
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