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- W2247307783 abstract "We give necessary and sufficient conditions for a real-valued quasiconvex function f on a Baire topological vector space X (in particular, Banach or Frechet space) to be continuous at the points of a residual subset of X. These conditions involve only simple topological properties of the lower level sets of f. A main ingredient consists in taking advantage of a remarkable property of quasiconvex functions relative to a topological variant of essential extrema on the open subsets of X. One application is that if f is quasiconvex and continuous at the points of a residual subset of X, then with a single possible exception, f^{-1}(a) is nowhere dense or has nonempty interior, as is the case for everywhere continuous functions. As a barely off-key complement, we also prove that every usc quasiconvex function is quasicontinuous in the (classical) sense of Kempisty since this interesting property does not seem to have been noticed before." @default.
- W2247307783 created "2016-06-24" @default.
- W2247307783 creator A5018713517 @default.
- W2247307783 date "2012-06-25" @default.
- W2247307783 modified "2023-09-27" @default.
- W2247307783 title "Points of continuity of quasiconvex functions on topological vector spaces" @default.
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