๐”– Bobbio Scriptorium
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A fixed box theorem for the cartesian product of graphs and metric spaces

โœ Scribed by Claude Tardif


Book ID
108316038
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
582 KB
Volume
171
Category
Article
ISSN
0012-365X

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We prove uniqueness of decomposition of a finite metric space into a product of metric spaces for a wide class of product operations. In particular, this gives the positive answer to the long-standing question of S. Ulam: 'If U ร— U V ร— V with U , V compact metric spaces, will then U and V be isometr

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The properties of certain sets called prefibers in a metric space are used to show that the algebraic properties of the Cartesian product of graphs generalize to metric spaces. Definition 1.1. (i) Let X = lJEIXi, for i E I, pri denotes the projection on Xi; for x E X, the i-fiber of X through x is