Simple Discontinuities: 10979
| Autor: | Donald P. Minassian, K. P. Hart |
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| Rok vydání: | 2004 |
| Předmět: | |
| Zdroj: | The American Mathematical Monthly. 111:630 |
| ISSN: | 0002-9890 |
| DOI: | 10.2307/4145177 |
| Popis: | (p ,n, p). From this it follows that d(f(x-), f(x)) < (2/3)2-n if x E A n (p Sp, p) and so indeed (p 6p, p) n An = 0. Now note that {(p Sp, p): p E An} is a pairwise disjoint family of intervals in the real line, and hence countable, which implies that An is countable. But A = U, An, so it follows that A is countable. The same argument shows that B is countable. It follows that D = A U B is countable. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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