Two large subsets of a functional space
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171285000199 |
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| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |