Vol. 28, No. 1, 1969

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On H-equivalence of uniformities. II

A. J. Ward

Vol. 28 (1969), No. 1, 207–215

This paper, continuing previous work by the same author, is concerned with the following problem: Given a metrisable uniformity U for a set X, does there exist another (distinct) uniformity B for X such that the two corresponding Hausdorff uniformities induce the same topology on the set, S(X) say, of all nonempty subsets of X? Sufficient conditions for the existence, and sufficient conditions for the nonexistence, of such a uniformity B are given, together with related results concerning the Hausdorff uniformities (derived from U and B) for S(X1), where X1 is a subset of X, everywhere dense in the topology derived from U.

Mathematical Subject Classification
Primary: 54.30
Received: 30 June 1966
Published: 1 January 1969
A. J. Ward