Metric inequalities and convexity
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- by Dorothy Wolfe
- Proc. Amer. Math. Soc. 40 (1973), 559-562
- DOI: https://doi.org/10.1090/S0002-9939-1973-0319045-9
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Abstract:
Conditions that a given point of a normed linear space is (or is not) a convex combination of $n$ fixed points are given in terms of the metric. The point is said to be metrically dependent if the conditions hold.References
- Russell G. Bilyeu, Metric definition of the linear structure, Proc. Amer. Math. Soc. 25 (1970), 205–206. MR 259562, DOI 10.1090/S0002-9939-1970-0259562-0
- Marshall Hall Jr., Combinatorial theory, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0224481
- Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR 0170264
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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