Vol. 40, No. 2, 1972

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The open mapping theorem for spaces with unique segments

James DeWitt Stein

Vol. 40 (1972), No. 2, 459–462

If X and Y are spaces with unique segments, an affine map from X into Y is a map which takes segments into segments. The purpose of this paper is to give conditions on spaces X and Y such that we can prove the following versions of the Open Mapping and Closed Graph Theorems: (1) a continuous affine map of X onto Y is open, and (2) an affine map of X onto Y with closed graph is continuous.

Mathematical Subject Classification 2000
Primary: 54C10
Secondary: 46A30, 54E35
Received: 28 October 1970
Published: 1 February 1972
James DeWitt Stein