Borel isomorphism

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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.


External links[edit]

Borel Spaces, by S. K. Berberian

Real Analysis and Probability, page 487, Second edition, by R. M. Dudley

A course on Borel sets by Sashi Mohan Srivastava