Borel isomorphism
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.
References
- Alexander S. Kechris, "Classical Descriptive Set Theory", Springer-Verlag, 1995
External links
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