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Embedding an analytic equivalence relation in the transitive closure of a Borel relation by Green, Edward J. is a scholarly article available to read on EtoBox.

What is Embedding an analytic equivalence relation in the transitive closure of a Borel relation about?

The transitive closure of a reflexive, symmetric, analytic relation is an analytic equivalence relation. Does some smaller class contain the transitive closure of every reflexive, symmetric, closed relation? An essentially negative answer is provided here. Every analytic equivalence relation on an arbitrary Polish space is Borel embeddable in the transitive closure of the union of two smooth Borel equivalence relations on that space. In the case of the Baire space, the two smooth relations are closed and the embedding is homeomorphic.

Author

Green, Edward J.

Published

2012

Language

EN