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Metric Spaces in Which All Triangles Are Degenerate

1997
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The American mathematical monthly
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In any subspace of the real line R with the usual Euclidean metric d(x, y) = |x − y|, every triangle is degenerate. In R 2 or R 3 with the usual Euclidean metrics, a triangle is degenerate if and only if its vertices are collinear. With our intuition of a degenerate triangle having "collinear vertices" extended to arbitrary metric spaces, we might expect that a metric space in which every triangle is degenerate must be "linear". It might be reasonable to expect that any "linear" metric space is

doi:10.2307/2975234
fatcat:zzij3gzcnncv3phchexpyeqzvu