BROUWER'S FAN THEOREM AND CONVEXITY

Berger, Josef and 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 {0, 1}*, 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 {0, 1}* 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
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-4812
• Language: English