A domain-theoretic investigation of posets of sub-sigma-algebras (extended abstract)

Ingo Battenfeld
(TU Dortmund)

Given a measurable space (X, M) there is a (Galois) connection between sub-sigma-algebras of M and equivalence relations on X. On the other hand equivalence relations on X are closely related to congruences on stochastic relations. In recent work, Doberkat has examined lattice properties of posets of congruences on a stochastic relation and motivated a domain-theoretic investigation of these ordered sets. Here we show that the posets of sub-sigma-algebras of a measurable space do not enjoy desired domain-theoretic properties and that our counterexamples can be applied to the set of smooth equivalence relations on an analytic space, thus giving a rather unsatisfactory answer to Doberkat's question.

In Xizhong Zheng and Ning Zhong: Proceedings Seventh International Conference on Computability and Complexity in Analysis (CCA 2010), Zhenjiang, China, 21-25th June 2010, Electronic Proceedings in Theoretical Computer Science 24, pp. 19–28.
Published: 3rd June 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.24.7 bibtex PDF

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