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Ideal-like properties of generalized microscopic sets. (English) Zbl 1399.28001

Summary: We show that not every family of generalized microscopic sets forms an ideal. Moreover, we prove that some of these families have some weaker additivity properties and some of them do not have even that.

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
03E15 Descriptive set theory
26A30 Singular functions, Cantor functions, functions with other special properties
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