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For questions from continuum theory. A continuum is a compact connected metric space (sometimes this term is used for a compact connected Hausdorff space).
2
votes
Can an "almost injective'' function exist between compact connected metric spaces?
Not a definite answer, but I have to join images. Since it needs some patience to get to my point, let me say that I suspects that examples verifying (1), (2) and (3) do exist.
Since you mention a dyn …