Brouwer’s Fan Theorem and Convexity

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

Abstract

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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-4812
• Alliance/National Licence: This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
• Language: English