Does every connected complete metric space with more than one point contain a non-trivial path? The pseudo-arc is an example of a connected metrizable space without a path.
2026-04-15 12:57:01.1776257821
Do connected complete metric spaces always contain a path?
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Such spaces do exist, since there are connected Polish spaces without non degenerate connected compact subsets. See the 1st answer to https://mathoverflow.net/questions/25171/how-thinly-connected-can-a-closed-subset-of-hilbert-space-be.