On a Map from a Function Space to a Hyperspace

E. Michael
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E. Michael: University of Washington, Department of Mathematics

A chapter in Contributions to Functional Analysis, 1966, pp 87-88 from Springer

Abstract: Abstract Let X be a metric space with metric d, and let K (X) be the space of non-empty, compact subsets of X, metrized by the Hausdorff metric % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe % e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj-hEeeu0xXdbba9fr % Fj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYx % e9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOaeaaaaaa % aaa8qabaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiuaa % cqWFXpq8caGGOaGaamyqaiaacYcacaWGcbGaaiykaiabg2da9iGac2 % gacaGGHbGaaiiEaiaacIcaciGGZbGaaiyDaiaacchadaWgaaWcbaGa % amiEaiabgIGiolaadgeaaeqaaOGaamizaiaacIcacaWG4bGaaiilai % aadkeacaGGPaGaaiilaiGacohacaGG1bGaaiiCamaaBaaaleaacaWG % 4bGaeyicI4SaamOqaaqabaGccaWGKbGaaiikaiaadIhacaGGSaGaam % yqaiaacMcacaGGPaGaaiOlaaaa!6389! $$\varrho (A,B) = \max ({\sup _{x \in A}}d(x,B),{\sup _{x \in B}}d(x,A)).$$

Date: 1966
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DOI: 10.1007/978-3-642-85997-7_2

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