Computability in Europe 2008
Logic and Theory of Algorithms

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Regular Talk:
Factoring out Intuitionistic Theorems: Continuity Principles and the Uniform Continuity Theorem

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Speaker: Iris Loeb
Slot: Tue, 12:20-12:40, Amphitheater A (col. 1)

Abstract

We prove the equivalence between some intuitionistic theorems and the
conjunction of a continuity principle and a compactness principle over
Bishop's Constructive Mathematics within the programme of Constructive
Reverse Mathematics.
To clarify our line of thought, we first point out the relation between
quasi-equicontinuity, quasi-uniform convergence, and the continuity principle
saying that the limit of a convergent sequence of continuous functions is again
continuous.
Finally, as a spin-off, we conclude that we have found a new, more economic
proof of the statement that every convergent sequence of functions on a compact
metric space converges uniformly.

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