¿If A and B are convex sets, is it true that the union of their interiors is equal to the interior of their unions?
2026-03-27 00:05:13.1774569913
Union of interiors of convex sets
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This question has been answered in the negative by the examples in the comments by @RedShoes, reproduced below.
No, consider $A = (-\infty,0]$ and $B = [0,\infty)$ as subsets of $\mathbb{R}$ in the usual topology.