Two large subsets of a functional space

F. S. Cater

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-3

Abstract:

Let P 1 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 D 0 consist of those functions in P that are unsigned on every interval, and let D 1 consist of those functions in P 1 that vanish on dense subsets of measure zero. Then D 0 and D 1 are dense G δ -subsets of P 1 with void interior. Neither D 0 nor D 1 is a subset of the other.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:931974

DOI: 10.1155/S0161171285000199

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