MathDB
Miklos Schweitzer 1978_4

Source:

January 25, 2009
functionlimitreal analysisreal analysis unsolved

Problem Statement

Let Q \mathbb{Q} and R \mathbb{R} be the set of rational numbers and the set of real numbers, respectively, and let f:Q→R f : \mathbb{Q} \rightarrow \mathbb{R} be a function with the following property. For every h∈Q,  x0∈R h \in \mathbb{Q} , \;x_0 \in \mathbb{R}, f(x\plus{}h)\minus{}f(x) \rightarrow 0 as x∈Q x \in \mathbb{Q} tends to x0 x_0. Does it follow that f f is bounded on some interval? M. Laczkovich
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