Injective metric space | Wikipedia audio article

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00:00:47 1 Hyperconvexity
00:02:09 2 Injectivity
00:03:03 3 Examples
00:03:51 4 Properties



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SUMMARY
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In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L∞ distances in higher-dimensional vector spaces. These properties can be defined in two seemingly different ways: hyperconvexity involves the intersection properties of closed balls in the space, while injectivity involves the isometric embeddings of the space into larger spaces. However it is a theorem of Aronszajn and Panitchpakdi (1956; see e.g. Chepoi 1997) that these two different types of definitions are equivalent.