MathDB
Miklos Schweitzer 1981_8

Source:

January 31, 2009
functiontopology

Problem Statement

Let W W be a dense, open subset of the real line R \mathbb{R}. Show that the following two statements are equivalent: (1) Every function f:R→R f : \mathbb{R} \rightarrow \mathbb{R} continuous at all points of R∖W \mathbb{R} \setminus W and nondecreasing on every open interval contained in W W is nondecreasing on the whole R \mathbb{R}. (2) R∖W \mathbb{R} \setminus W is countable. E. Gesztelyi
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