Abstract
The classical statement of Dini’s Theorem on the uniform convergence of increasing sequences of continuous functions cannot be proved constructively, since it fails in the recursive model. Nevertheless, a basic constructive version of the theorem is proved, as is a version in which the uniform convergence of the sequence of functions is reduced to the convergence of some subsequence of a particular sequence of real numbers. After some additional reductions and conjectures related to Dini’s Theorem, the paper ends by showing that a particular version of the theorem implies a weak Heine-Borel-Lebesgue Theorem.
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Bridges, D.S. (2001). Dini’s Theorem: A Constructive Case Study. In: Calude, C.S., Dinneen, M.J., Sburlan, S. (eds) Combinatorics, Computability and Logic. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0717-0_7
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DOI: https://doi.org/10.1007/978-1-4471-0717-0_7
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