Generalized Helly spaces, continuity of monotone functions, and metrizing maps
نویسندگان
چکیده
منابع مشابه
Continuity of Monotone Functions
Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. ...
متن کاملMonotone Functions and Maps
In [1] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals (e.g., real semialgebraic or subanalytic sets), and having connected intersections with all translated coordinate cones in Rn. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equ...
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Recent characterizations of various types of differentiable generalized monotone maps by Karamardian– Schaible–Crouzeix and their strengthened versions by Crouzeix–Ferland are extended to the nonsmooth case. For nondifferentiable locally Lipschitz maps necessary and/or sufficient conditions for quasimonotonicity, pseudomonotonicity and strict/ strong pseudomonotonicity are derived. To accomplis...
متن کاملCone Monotone Functions: Differentiability and Continuity
We provide a porosity based approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of the continuous functions.
متن کاملA 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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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2008
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm200-2-4