Vol. 66, No. 2, 1976

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A generalization of the unit interval

William M. Cornette

Vol. 66 (1976), No. 2, 313–323
Abstract

Convex sets are discussed here in linear spaces over scalars other than the reals. To facilitate this development, the interval [0,1] is generalized to a unit interval in an arbitrary division ring. The interval [0,1] is shown to be the maximum generalized unit interval in the real number field, the complex number field, and the quaternion division ring. Several elementary theorems on convexity are proved for linear spaces over scalars having generalized unit intervals of certain types.

Mathematical Subject Classification 2000
Primary: 52A05
Milestones
Received: 10 May 1974
Revised: 7 June 1976
Published: 1 October 1976
Authors
William M. Cornette