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MB-representations and topological algebras. (English) Zbl 1049.28001

Summary: For an algebra \(\mathcal A\) and an ideal \(\mathcal I\) of subsets of a set \(X\) we consider pairs \(\langle{\mathcal A},{\mathcal I}\rangle\) which have the common inner Marczewski-Burstin representation. The main goal of the paper is to investigate which inner Marczewski-Burstin representable algebras and pairs are topological.

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
03E20 Other classical set theory (including functions, relations, and set algebra)
03E35 Consistency and independence results
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
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