A topological characterization of the existence of non-empty choice sets
| Autor: | Eleftherios Zacharias, Athanasios Andrikopoulos |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Generalized Top-Choice Assumption
Discrete mathematics Binary relation Upper semicontinuity R-upper compactness Generalized Optimal-Choice Axiom Generalized Top-Choice Assumption Smith set Schwartz set Maximal elements Acyclicity Smith set Characterization (mathematics) Schwartz set Topology Acyclicity Maximal elements Generalized Optimal-Choice Axiom R-upper compactness Choice function Geometry and Topology Upper semicontinuity Social choice theory Finite set Maximal element Mathematics |
| Zdroj: | Topology and its Applications. 159:1987-1992 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2011.04.030 |
| Popis: | The theory of optimal choice sets is a solution theory that has a long and well-established tradition in social choice and game theories. In this paper, we characterize the existence of the most important solution theories of arbitrary binary relations over non-finite sets of alternatives. More precisely, we present a topological characterization of the Smith and Schwartz sets. We also generalize results of the above solution theories for asymmetric binary relations defined in finite sets as well as most of the known results concerning the (characterization of the) existence of maximal elements of binary relations on compact spaces. Topology and its Applications |
| Databáze: | OpenAIRE |
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