Abstract
Compactness is an important topological property as it enables us to apply minimax theorems in economic theory. The theory of optimal choice sets is a solution theory that has a long and well-established tradition in social choice and game theories. A general solution concept of choice problems when the set of best alternatives does not exist (this problem occurs when the preferences yielded by an economic process are cyclic) is the Schwartz set. This set is one of the most popular solution concepts since it insures rationality. The Schwartz set is equivalent to the admissible set that appears in the game theory literature. The present note shows that the feasible set is compact if and only if every generalized upper tc-semicontinuous preference has non-empty Schwartz (admissible) set.
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