pow:problem5f22
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| pow:problem5f22 [2022/11/08 06:36] – created mazur | pow:problem5f22 [2022/11/14 15:13] (current) – mazur | ||
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| + | <box 85% round orange| Problem 5 (due on Monday, November 7)> | ||
| + | Let $\cal F$ be the set of all functions $f:\mathbb R\longrightarrow \mathbb N$ from the real numbers to natural numbers. | ||
| + | Prove that there exists a sequence of functions $f_1,f_2, f_3,\ldots$ in $\cal F$ such that for every finite | ||
| + | set $A\subseteq \mathbb R$ and every $g\in \cal F$ there is $i$ such that $g(a)=f_i(a)$ for every $a\in A$. | ||
| + | </ | ||
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| + | The problem was solved by Levi Axelrod and Ashton Keith. The solutions differ in details but follow similar | ||
| + | idea. For a detailed solution and some applications to topology see the following link {{: | ||