The minimization property for spaces that are normed over semifields

A. I. Vasil'ev

Ural State University

Abstract: We show that if each nonempty subset of a space $X$, normed over a pair of topological semifields, has the minimization property, then $X$ is a real normed space (up to an isomorphism).

UDC: 517.83

Received: 13.06.1968

 English version: Mathematical Notes, 1969, 5:3, 180–183

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