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In the earliest days of MathOverflow, there was a '20 questions' seminar (see <http://sbseminar.wordpress.com/category/20-questions/>) run by graduate students at Berkeley. Many questions from the seminar were cross-posted to MathOverflow. This tag now exists solely for the historical record.

62 votes

Can you explicitly write $\mathbb{R}^2$ as a disjoint union of two totally path disconnected...

Let $S$ be a subset of the reals such that $S \cap [a,b]$ and $S^c \cap [a,b]$ cannot be written as a countable union of closed sets for any $a < b$. This can be done (this explicit example of a non-B …
George Lowther's user avatar