Intersection Theorems with a Continuum of Intersection Points
| Autor: | P.J.J. Herings, A.J.J. Talman |
|---|---|
| Přispěvatelé: | Research Group: Economics, Research Group: Operations Research |
| Rok vydání: | 1998 |
| Předmět: |
Intersection theorem
Pure mathematics Optimization operations research Control and Optimization Continuum (topology) Generalization Applied Mathematics Mathematics::General Topology Management Science and Operations Research Intersection graph Convexity Combinatorics Intersection Unit cube Finite intersection property Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications, 96(2), 311-335. SPRINGER/PLENUM PUBLISHERS |
| ISSN: | 1573-2878 0022-3239 |
| DOI: | 10.1023/a:1022618130893 |
| Popis: | In all existing intersection theorems, conditions are given under which a certain subset of a collection of sets has a nonempty intersection. In this paper, conditions are formulated under which the intersection is a continuum of points satisfying some interesting topological properties. In this sense, the intersection theorems considered in this paper belong to a new class. The intersection theorems are formulated on the unit cube and it is shown that both the vector of zeroes and the vector of ones lie in the same component of the intersection. An interesting application concerns the model of an economy with price rigidities. Using the intersection theorems of this paper, it is easily shown that there exists a continuum of zero points in such a model. The intersection theorems treated give a generalization of the well-known lemmas of Knaster, Kuratowski, and Mazurkiewicz (Ref. 1), Scarf (Ref. 2), Shapley (Ref. 3), and Ichiishi (Ref. 4). Moreover, the results can be used to sharpen the usual formulation of the Scarf lemma on the cube. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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