In:
The Journal of Symbolic Logic, Cambridge University Press (CUP), Vol. 83, No. 04 ( 2018-12), p. 1363-1375
Abstract:
In the framework of Bishop’s constructive mathematics we introduce co-convexity as a property of subsets B of ${\left\{ {0,1} \right\}^{\rm{*}}}$ , 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 ${\left\{ {0,1} \right\}^{\rm{*}}}$ 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.
Type of Medium:
Online Resource
ISSN:
0022-4812
,
1943-5886
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2018
detail.hit.zdb_id:
2010607-5
SSG:
5,1
SSG:
17,1
