If I take the Cantor ternary set constructed on the interval $[0,1]$ and collapse the spaces between the points of the Cantor set, do I obtain an interval again? My intuition tells me that it should be so because the Cantor set is equipotent to the interval $[0,1]$, but I'm not sure how to prove it. Essentially, is the collapsed Cantor set homeomorphic to the interval $[0,1]$?
2026-03-27 07:48:29.1774597709
Is the collapsed Cantor set homeomorphic to the interval $[0,1]$?
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