Vol. 55, No. 1, 1974

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ISSN: 0030-8730
Measurable uniform spaces

Zdeněk Frolík

Vol. 55 (1974), No. 1, 93–105
Abstract

A uniform space is called 0-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
Authors
Zdeněk Frolík