Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1363-1375 |
| Seitenumfang | 13 |
| Fachzeitschrift | Journal of Symbolic Logic |
| Jahrgang | 83 |
| Ausgabenummer | 4 |
| Frühes Online-Datum | 21 Dez. 2018 |
| Publikationsstatus | Veröffentlicht - Dez. 2018 |
| Extern publiziert | Ja |
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.
ASJC Scopus Sachgebiete
- Geisteswissenschaftliche Fächer (insg.)
- Philosophie
- Mathematik (insg.)
- Logik
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in: Journal of Symbolic Logic, Jahrgang 83, Nr. 4, 12.2018, S. 1363-1375.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Brouwer's fan theorem and convexity
AU - Berger, Josef
AU - Svindland, G.
N1 - Publisher Copyright: © The Association for Symbolic Logic 2018.
PY - 2018/12
Y1 - 2018/12
N2 - 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.
AB - 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.
KW - constructive mathematics
KW - convex functions
KW - fan theorem
UR - http://www.scopus.com/inward/record.url?scp=85061910614&partnerID=8YFLogxK
U2 - 10.1017/jsl.2018.49
DO - 10.1017/jsl.2018.49
M3 - Article
VL - 83
SP - 1363
EP - 1375
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
SN - 0022-4812
IS - 4
ER -