Vol. 26, No. 3, 1968

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A locally convex topology on a preordered space

Marvin D. Green

Vol. 26 (1968), No. 3, 487–491

The purpose of this paper is to introduce a locally convex topology 𝒯c on a preordered topological space (X,𝒯 ) in such a way that, if 𝒯c is weaker than 𝒯 , then it is the l.u.b. of all locally convex topologies weaker than 𝒯 . Some of the consequences of having such a topology defined are examined, and the concepts of c-continuity and c-limit of a function are introduced. As an application of the machinery developed, a theorem concerning the unique extendability of functions from dense subsets of preordered spaces into regularly preordered spaces is established.

Mathematical Subject Classification
Primary: 54.56
Received: 5 October 1967
Published: 1 September 1968
Marvin D. Green