Vol. 47, No. 1, 1973

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The strict topology, separable measures, and paracompactness

Robert Francis Wheeler

Vol. 47 (1973), No. 1, 287–302

The theory of the strict topology β on C(X) has recently been extended to a completely regular setting by Sentilles. Here it is shown that equality of the separable and τ-additive Baire measures on X is a sufficient condition for (C(X)) to be a strong Mackey space. As a consequence, the Conway-LeCam Theorem for paracompact spaces is extended to the completely regular case. A locally convex topology βe on C(X) is considered; βe is strong Mackey, and the dual space is the space of separable measures. Results of Dudley, Granirer, and Leger and Soury on convergence in the space of measures are unified and extended in this context.

Mathematical Subject Classification 2000
Primary: 46E10
Received: 12 April 1972
Published: 1 July 1973
Robert Francis Wheeler