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About Bernstein sets
Remember that a subset $X\subseteq \mathbb{R}$ is a $G_{\delta}$-set if $X$ is a countable intersection of open sets in $\mathbb{R}$. For example closed subsets of $\mathbb{R}$ are $G_{\delta}$-sets. ...
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Is axiom of choice required to throw away repeated intervals in a constructive argument?
I am looking at this answer to this question:
Let $U \subseteq \mathbb{R}$ be open and let $x \in U$. Either $x$ is rational or irrational. If $x$ is rational, define
\begin{align}I_x = \bigcup\...
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