Metric inequalities and convexity
Author:
Dorothy Wolfe
Journal:
Proc. Amer. Math. Soc. 40 (1973), 559-562
MSC:
Primary 52A05
DOI:
https://doi.org/10.1090/S0002-9939-1973-0319045-9
MathSciNet review:
0319045
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Abstract | References | Similar Articles | Additional Information
Abstract: Conditions that a given point of a normed linear space is (or is not) a convex combination of 
fixed points are given in terms of the metric. The point is said to be metrically dependent if the conditions hold.
- [1] Russell G. Bilyeu, Metric definition of the linear structure, Proc. Amer. Math. Soc. 25 (1970), 205–206. MR 0259562, https://doi.org/10.1090/S0002-9939-1970-0259562-0
- [2] Marshall Hall Jr., Combinatorial theory, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0224481
- [3] Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR 0170264
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0319045-9
Keywords:
Normed linear space,
metric space,
convex combinations,
extreme points
Article copyright:
© Copyright 1973
American Mathematical Society
