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Descriptive Set Theory is the study of
structures and the relations of sets in a Polish space. A Polish space
is a metric space which is separable and complete. It is easy to see that the cardinality
of a Polish space is at
most continuum because of the separability condition. The most typical examples of
Polish spaces are Rn,
w (the set of natural
numbers with discrete topology), the Cantor space w2, and the Baire space ww.
For more examples and discussions on Polish spaces, the
reader can consult the following two excellent
texts on this topic.
Y. N. Moschovakis, Descriptive Set theory North-Holland,
A. S. Kechris, Classical Descriptive Set