Real Analysis Exchange

Approximately Continuous Functions Have Approximate Extrema, a New Proof

Chris Freiling, Paul D. Humke, and Richard J. O'Malley

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In 1975, Richard O’Malley proved that every approximately continuous function has approximate extrema, and this result provides an immediate solution to SB 157. The purpose of this paper is to provide an additional proof of O’Malley's result.

Article information

Real Anal. Exchange, Volume 41, Number 2 (2016), 409-414.

First available in Project Euclid: 30 March 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
Secondary: 26A48: Monotonic functions, generalizations

approximate maximum approximate continuity


Freiling, Chris; Humke, Paul D.; O'Malley, Richard J. Approximately Continuous Functions Have Approximate Extrema, a New Proof. Real Anal. Exchange 41 (2016), no. 2, 409--414.

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