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Set-valued and variational analysis, ISSN 1877-0541, 2017, Volume 26, Issue 1, pp. 49 - 65
... convergence on the bornology of totally bounded subsets. We identify a new bornology for a metric space containing the bornology of Bourbaki bounded sets on which uniform convergence preserves uniform continuity... 
Secondary 54E50, 54E35 | Totally bounded set | Relatively compact set | Probability Theory and Stochastic Processes | Mathematics | Continuous function | Bornology | Primary 54C35, 26A16, 46A17 | Analysis | Ring of functions | Bourbaki bounded set | Lipschitz function | Infinitely nonuniformly isolated set | Cauchy continuous function | Uniformly continuous function | UC-space | MATHEMATICS, APPLIED
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