Vol. 99, No. 2, 1982

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ISSN: 0030-8730
Continuity of monotone functions

Mark Mandelker

Vol. 99 (1982), No. 2, 413–418
Abstract

Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. Any monotone pointwise continuous function is uniformly continuous. Continuous inverse functions are also obtained. The methods used are in accord with the principles of Bishop’s Foundations of Constructive Analysis, 1967.

Mathematical Subject Classification 2000
Primary: 26A48
Secondary: 03F65
Milestones
Received: 3 September 1980
Revised: 11 February 1981
Published: 1 April 1982
Authors
Mark Mandelker