Metric Spaces
نویسنده
چکیده
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, let X = R and take
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