We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to “extend” a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions are satisfied.
De Bernardi, C. A., On the Extension of Continuous Quasiconvex Functions, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2020; 187 (2): 421-430. [doi:10.1007/s10957-020-01767-x] [http://hdl.handle.net/10807/164335]
On the Extension of Continuous Quasiconvex Functions
De Bernardi, Carlo Alberto
2020
Abstract
We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to “extend” a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions are satisfied.
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