This is a question related to my last; I have still not solved it. Maybe this one is easier:
Suppose $X$ is a connected complete metric space with more than one point. Must $X$ contain a non-singleton non-empty connected $G_\delta$ proper subset?
2026-04-17 10:58:45.1776423525
Connected $G_\delta$ non-singleton, proper subsets in a connected complete metric space with more than one point
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