Convexity and constructive infima

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Josef Berger
  • G. Svindland

Externe Organisationen

  • Ludwig-Maximilians-Universität München (LMU)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)873-881
Seitenumfang9
FachzeitschriftArchive for mathematical logic
Jahrgang55
Ausgabenummer7-8
PublikationsstatusVeröffentlicht - 1 Nov. 2016
Extern publiziertJa

Abstract

We show constructively that every quasi-convex uniformly continuous function f: C → R + has positive infimum, where C is a convex compact subset of R n. This implies a constructive separation theorem for convex sets.

ASJC Scopus Sachgebiete

Zitieren

Convexity and constructive infima. / Berger, Josef; Svindland, G.
in: Archive for mathematical logic, Jahrgang 55, Nr. 7-8, 01.11.2016, S. 873-881.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Berger J, Svindland G. Convexity and constructive infima. Archive for mathematical logic. 2016 Nov 1;55(7-8):873-881. doi: 10.1007/s00153-016-0502-y
Berger, Josef ; Svindland, G. / Convexity and constructive infima. in: Archive for mathematical logic. 2016 ; Jahrgang 55, Nr. 7-8. S. 873-881.
Download
@article{7143a1193ed44a1f8b0306d609aac630,
title = "Convexity and constructive infima",
abstract = "We show constructively that every quasi-convex uniformly continuous function f: C → R + has positive infimum, where C is a convex compact subset of R n. This implies a constructive separation theorem for convex sets.",
keywords = "Bishop{\textquoteright}s constructive mathematics, Brouwer{\textquoteright}s fan theorem, Convex functions, Separating hyperplanes",
author = "Josef Berger and G. Svindland",
note = "Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",
year = "2016",
month = nov,
day = "1",
doi = "10.1007/s00153-016-0502-y",
language = "English",
volume = "55",
pages = "873--881",
journal = "Archive for mathematical logic",
issn = "0933-5846",
publisher = "Springer New York",
number = "7-8",

}

Download

TY - JOUR

T1 - Convexity and constructive infima

AU - Berger, Josef

AU - Svindland, G.

N1 - Publisher Copyright: © 2016, Springer-Verlag Berlin Heidelberg.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - We show constructively that every quasi-convex uniformly continuous function f: C → R + has positive infimum, where C is a convex compact subset of R n. This implies a constructive separation theorem for convex sets.

AB - We show constructively that every quasi-convex uniformly continuous function f: C → R + has positive infimum, where C is a convex compact subset of R n. This implies a constructive separation theorem for convex sets.

KW - Bishop’s constructive mathematics

KW - Brouwer’s fan theorem

KW - Convex functions

KW - Separating hyperplanes

UR - http://www.scopus.com/inward/record.url?scp=84984795708&partnerID=8YFLogxK

U2 - 10.1007/s00153-016-0502-y

DO - 10.1007/s00153-016-0502-y

M3 - Article

VL - 55

SP - 873

EP - 881

JO - Archive for mathematical logic

JF - Archive for mathematical logic

SN - 0933-5846

IS - 7-8

ER -