Borel isomorphism

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In mathematics, Borel isomorphism is a Borel measurable bijective function from one Polish space to another Polish space. Borel isomorphisms are closed under composition and under taking of inverses. The set of Borel isomorphisms from a Polish space to itself apparently forms a group under composition. Borel isomorphisms on Polish spaces are analogous to homeomorphisms on topological spaces: both are bijective and closed under composition, and a homeomorphism and its inverse are both continuous, instead of both being Borel measurable.

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External links[edit]

Borel Spaces, by S. K. Berberian http://www.ma.utexas.edu/mp_arc/c/02/02-156.pdf

Real Analysis and Probability, page 487, Second edition, by R. M. Dudley http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511755347&cid=CBO9780511755347A091

A course on Borel sets by Sashi Mohan Srivastava http://books.google.com/books?id=FhYGYJtMwcUC&pg=PA169