Is there an easy (but nontrivial) example of an inverse limit of real, closed intervals, which is an open interval, and for which at least one of the projections is a surjection ?
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2026-03-25 00:01:10.1774396870
Inverse limit of closed intervals which is open?
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An inverse limit of compact Hausdorff spaces is compact, because the product of those spaces is compact (by Tychonoff's Theorem) and Hausdorff, and the inverse limit is a closed subset of the product. So no, this is not possible.