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

Zbigniew Fiedorowicz

Vol. 34 (1970), No. 1, 51–60

DOI: 10.2140/pjm.1970.34.51

Abstract

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

Milestones

Received: 19 August 1969

Published: 1 July 1970