Using a definition I saw in an old Russian book, a set in $\mathcal R^{n}$ is said to be connected if it cannot be represented as a disjoint union of two nonempty, separated sets. Separated, meaning the intersection of the closure of each one with the other set is an empty set. Odlly enough, by this definition the set mentioned in the title is connected, which is not very intuitive. I might be wrong. If anyone has anything to clear me up, a graphical approach is much appreciate.
2026-03-28 02:10:34.1774663834
Connectedness of circle without center line across it
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