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Berger, Josef and Svindland, Gregor (2018): Brouwer’s Fan Theorem and Convexity. In: Journal of Symbolic Logic, Vol. 83, No. 4: pp. 1363-1375 [PDF, 152kB]


In the framework of Bishop’s constructive mathematics we introduce co-convexity as a property of subsets B of , the set of finite binary sequences, and prove that co-convex bars are uniform. Moreover, we establish a canonical correspondence between detachable subsets B of and uniformly continuous functions f defined on the unit interval such that B is a bar if and only if the corresponding function f is positive-valued, B is a uniform bar if and only if f has positive infimum, and B is co-convex if and only if f satisfies a weak convexity condition.

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