Details
| Original language | English |
|---|---|
| Pages (from-to) | 873-881 |
| Number of pages | 9 |
| Journal | Archive for mathematical logic |
| Volume | 55 |
| Issue number | 7-8 |
| Publication status | Published - 1 Nov 2016 |
| Externally published | Yes |
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’s constructive mathematics, Brouwer’s fan theorem, Convex functions, Separating hyperplanes
ASJC Scopus subject areas
- Arts and Humanities(all)
- Philosophy
- Mathematics(all)
- Logic
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In: Archive for mathematical logic, Vol. 55, No. 7-8, 01.11.2016, p. 873-881.
Research output: Contribution to journal › Article › Research › peer review
}
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 -