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The open mapping
theorem for spaces with unique segments
James DeWitt Stein |
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Vol. 40 (1972), No. 2, 459–462
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Abstract |
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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
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Milestones
Received: 28 October 1970
Published: 1 February 1972
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Authors |
| James DeWitt Stein | |
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