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Jun 3, 2021 at 20:06 comment added Jeremy Brazas So any path-connected, separable, but non-analytic metric space would do. Really nice! If you find an argument with for the possibility mentioned in your comment, please let me know.
Jun 3, 2021 at 19:55 vote accept Jeremy Brazas
Jun 3, 2021 at 14:40 comment added Benjamin Vejnar It could be possibly true that every path-connected separable analytic metric space is homeomorphic to a path component of a compact metric space.
Jun 2, 2021 at 14:33 comment added Joel David Hamkins This is great !
Jun 2, 2021 at 13:35 history answered Benjamin Vejnar CC BY-SA 4.0