Abstract
We show that it is consistent that there is a hereditarily separable, 0-dimensional T2 space X of cardinality ω1 such that for each uncountable subspace Y of X there is a continuous bijection φ : Y → X and there is a partition (Yi)i<n of Y into finitely many pieces such that φ ↾ Yi is a homeomorphism for each i < n.
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