Perfect set property

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.

Perfect set property - Wikipedia Jump to content From Wikipedia, the free encyclopedia Property in descriptive set theory 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 . As nonempty perfect sets in a Polish space always have the cardinality of the continuum , and the reals form a Polish space, a set of reals with the perfect set property cannot be a counterexample to th

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