Measurable uniform spaces

Zdeněk Frolík

Vol. 55 (1974), No. 1, 93–105

DOI: 10.2140/pjm.1974.55.93

Abstract

A uniform space is called ℵ₀-measurable if the pointwise limit of any sequence of uniformly continuous functions (real valued) is uniformly continuous. A uniform space is called measurable if the pointwise limit of any sequence of uniformly continuous mappings into any metric space is uniformly continuous.

It is shown that measurable spaces are just metric-fine spaces with the property that the cozero sets form a σ-algebra, or just hereditarily metric-fine spaces.

Mathematical Subject Classification 2000

Primary: 54E15

Secondary: 28A05, 04A15

Milestones

Received: 2 March 1973

Published: 1 November 1974