Borel isomorphism
In mathematics, Borel isomorphism is a bijective Borel 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 clearly 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.
References
- Alexander S. Kechris (1995) Classical Descriptive Set Theory, Springer-Verlag.
External links
- S. K. Berberian (1988) Borel Spaces from University of Texas
- Richard M. Dudley (2002) Real Analysis and Probability, 2nd edition, page 487.
- Sashi Mohan Srivastava (1998) A Course on Borel Sets
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