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Descriptive set theory
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=== Regularity properties of Borel sets === Classical descriptive set theory includes the study of regularity properties of Borel sets. For example, all Borel sets of a Polish space have the [[property of Baire]] and the [[perfect set property]]. Modern descriptive set theory includes the study of the ways in which these results generalize, or fail to generalize, to other classes of subsets of Polish spaces.
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