I was wondering if the union of two disjoint arc connected spaces can be arc connected arc connected but i can't seem to find a proof or simply an example.
2026-03-27 10:31:34.1774607494
Can the union of two disjoint arc connected spaces be arc connected?
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$[0,1]$ and $(1,2]$ are arc connected and disjoint. Its union is $[0,2]$, also arc connected.