Abstract
Let P1 denote the Banach space composed of all bounded derivatives f of everywhere differentiable functions on [0, 1] such that the set of points where f vanishes is dense in [0, 1]. Let D0 consist of those functions in P that are unsigned on every interval, and let D1 consist of those functions in P1 that vanish on dense subsets of measure zero. Then D0 and D1 are dense Gδ‐subsets of P1 with void interior. Neither D0 nor D1 is a subset of the other.
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