Approximately continuous functions have approximate extrema, a new proof. (English) Zbl 1384.26022

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


26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A48 Monotonic functions, generalizations
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