A Helly-Type Theorem for Semi-monotone Sets and Monotone Maps
نویسندگان
چکیده
منابع مشابه
A Helly-Type Theorem for Semi-monotone Sets and Monotone Maps
We consider sets and maps defined over an o-minimal structure over the reals, such as real semi-algebraic or globally subanalytic sets. A monotone map is a multi-dimensional generalization of a usual univariate monotone continuous function on an open interval, while the closure of the graph of a monotone map is a generalization of a compact convex set. In a particular case of an identically con...
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A coordinate cone in R n is an intersection of some coordinate hy-perplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of R n , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This can be viewed as a generalization of the convexity property. Semi-monotone sets have a numb...
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† ENSTA, 32 Bd. Victor, 78539 Paris Cédex 15, France. Email: [email protected] Abstract: We consider convex maps f : Rn → Rn that are monotone (i.e., that preserve the product ordering of Rn ), and non-expansive for the sup-norm. This includes convex monotone maps that are additively homogeneous (i.e., that commute with the addition of constants). We show that the fixed point set of f ,...
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We consider convex maps that are monotone (i.e., that preserve the product ordering of ), and nonexpansive for the sup-norm. This includes convex monotone maps that are additively homogeneous (i.e., that commute with the addition of constants). We show that the fixed point set of , when it is non-empty, is isomorphic to a convex inf-subsemilattice of , whose dimension is at most equal to the nu...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2013
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-013-9540-y