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A Proof of Constructive Version of Brouwer's Fixed Point Theorem with Uniform Sequential Continuity

2011
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ISRN Applied Mathematics
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It is often said that Brouwer's fixed point theorem cannot be constructively proved. On the other hand, Sperner's lemma, which is used to prove Brouwer's theorem, can be constructively proved. Some authors have presented a constructive (or an approximate) version of Brouwer's fixed point theorem using Sperner's lemma. They, however, assume uniform continuity of functions. We consider uniform sequential continuity of functions. In classical mathematics, uniform continuity and uniform sequential

doi:10.5402/2011/276040
fatcat:ehk56pppyrh35by5rbmrpiqiji