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- W1517066694 abstract "We investigate choice principles in the Weihrauch lattice for finite sets on the one hand, and convex sets on the other hand. Increasing cardinality and increasing dimension both correspond to increasing Weihrauch degrees. Moreover, we demonstrate that the dimension of convex sets can be characterized by the cardinality of finite sets encodable into them. Precisely, choice from an n + 1 point set is reducible to choice from a convex set of dimension n, but not reducible to choice from a convex set of dimension n - 1. Furthermore we consider searching for zeros of continuous functions, and demonstrate that having finitely many zeros is a strictly weaker condition than having finitely many local extrema." @default.
- W1517066694 created "2016-06-24" @default.
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- W1517066694 date "2013-02-02" @default.
- W1517066694 modified "2023-09-27" @default.
- W1517066694 title "Closed choice: Cardinality vs convex dimension" @default.
- W1517066694 hasPublicationYear "2013" @default.
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