𝜀-continuity and monotone operations

William H. Julian

Vol. 115 (1984), No. 2, 385–390

DOI: 10.2140/pjm.1984.115.385

Abstract

We prove constructively in the sense of Bishop that a monotone, 𝜀-continuous operation from [0,1] into a metric space is 2𝜀-uniformly continuous. We derive a suitable version of Brouwer’s fan theorem.

Mathematical Subject Classification 2000

Primary: 46R05, 46R05

Secondary: 03F65, 26E99, 54C30

Milestones

Received: 28 April 1983

Published: 1 December 1984