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Line 12: * Every Polish space is [[homeomorphic]] to a ''G''<sub>δ</sub> [[subspace topology\|subspace]] of the [[Hilbert cube]], and every ''G''<sub>δ</sub> subspace of the Hilbert cube is Polish. * Every Polish space is obtained as a continuous image of ~~Bairse~~Baire space; in fact every Polish space is the image of a continuous bijection defined on a closed subset of Baire space. Similarly, every compact Polish space is a continuous image of Cantor space. Because of these universality properties, and because the Baire space <math>\mathcal{N}</math> has the convenient property that it is homeomorphic to <math>\mathcal{N}^\omega</math>, many results in descriptive set theory are proved in the context of Baire space alone.

Descriptive set theory: Difference between revisions