Logo Logo
Switch Language to German
Berger, Josef; Svindland, Gregor (2018): BROUWER'S FAN THEOREM AND CONVEXITY. In: Journal of Symbolic Logic, Vol. 83, No. 4: pp. 1363-1375
Full text not available from 'Open Access LMU'.


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.