منابع مشابه
Hyperbolizing Metric Spaces
It was proved by M. Bonk, J. Heinonen and P. Koskela that the quasihyperbolic metric hyperbolizes (in the sense of Gromov) uniform metric spaces. In this paper we introduce a new metric that hyperbolizes all locally compact noncomplete metric spaces. The metric is generic in the sense that (1) it can be defined on any metric space; (2) it preserves the quasiconformal geometry of the space; (3) ...
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Example 1.2. a) Let X = R and take d(x, y) = |x − y|. This is the most basic and important example. b) More generally, let N ≥ 1, let X = R , and take d(x, y) = ||x − y|| = √∑N i=1(xi − yi). It is very well known but not very obvious that d satisfies the triangle inequality. This is a special case of Minkowski’s Inequality, which will be studied later. c) More generally let p ∈ [1,∞), let N ≥ 1...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-10857-8