||This article may be too technical for most readers to understand. (November 2011)|
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.
- Alexander S. Kechris, "Classical Descriptive Set Theory", Springer-Verlag, 1995
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