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In the mathematical field of descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty perfect subset (Kechris 1995, p. 150). Note that having the perfect set property is not the same as being a perfect set.
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set perfect property space polish every countable sets subset reals uncountable disjoint union nonempty displaystyle form written axiom choice existence
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