Abstract
Stability of Effectivity Functions on a Topological Space of Alternatives is considered. Previous results proved by two authors are related to each other. Special attention is brought to the notions of cycle, upper and lower cycle. Examples of EFs with an infinite alternative space in Social Choice and Economic Theory are provided. Finally we prove by a direct method that the core of a Convex Topological EF is nonempty for any continuous preference relation.
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