Vol. 34, No. 1, 1970

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A comparison of two naturally arising uniformities on a class of pseudo-PM spaces

Zbigniew Fiedorowicz

Vol. 34 (1970), No. 1, 51–60

In this paper, we shall consider an important class of probabilistic pseudometric spaces, the so-called pseudometrically generated spaces, i.e., spaces with a collection of pseudometrics on which a probability measure has been defined. Specifically, we shall examine the relationship between the uniformity introduced on the space probabilistically by means of the socalled 𝜖,λ uniform neighborhoods and the uniformity obtained by considering all the uniform neighborhoods generated by each of the pseudometrics as a subbase.

Mathematical Subject Classification
Primary: 54.35
Secondary: 60.00
Received: 19 August 1969
Published: 1 July 1970
Zbigniew Fiedorowicz
Department of Mathematics
The Ohio State University
100 Mathematics building
231 West 18th Avenue
Columbus OH 43210-1174
United States