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arXiv · 1006.0393

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

Ingo Battenfeld
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Abstract

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.

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Ingo Battenfeld. 2010-06-02. A domain-theoretic investigation of posets of sub-sigma-algebras (extended abstract). https://doi.org/10.4204/eptcs.24.7

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