منابع مشابه
means of continuous selections ∗
If a discrete subset S of a topological group G with the identity 1 generates a dense subgroup of G and S ∪ {1} is closed in G, then S is called a suitable set for G. We apply Michael’s selection theorem to offer a direct, self-contained, purely topological proof of the result of Hofmann and Morris [8] on the existence of suitable sets in locally compact groups. Our approach uses only elementar...
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متن کاملContinuous selections of trajectories of hybrid systems
We present results on existence of continuous selections of trajectories of hybrid systems evolving according to Lipschitz nonlinear inclusions. First, we utilize the Skorohod metric to de4ne both a family of pseudo-metrics and a metric on the set of trajectories accepted by the hybrid automaton. We show that under a non-Zeno condition the latter metric is complete. Second, the existence of con...
متن کاملGroupwise dense families
We show that the Filter Dichotomy Principle implies that there are exactly four classes of ideals in the set of increasing functions from the natural numbers. We thus answer two open questions on consequences of < . We show that < implies that = , and that Filter Dichotomy together with < implies < . The technical means is the investigation of groupwise dense sets, ideals, filters and ultrafilt...
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Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as fully lower semicontinuous closed convex-valued mappings that arise in variational analysis and optimization of integral functionals. The characterization allo...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1959
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-47-2-173-178