Descriptive topological spaces and perfect maps

A complete regular Hausdorff space X is Cech-analytic if it is the projection of a Cech-complete subspace C $\subset {X} \times \ \omega\sp\omega$ along the so-called Baire space $\omega\sp\omega.$ We show that a perfect image of a Cech-analytic space is again Cech-analytic. This settles a question raised by the late Zdenek Frolik.

A completely regular Hausdorff space X is said to be partition analytic if it is the projection of a partition complete subspace C $\subset {X} \times \ \omega\sp\omega$ along $\omega\sp\omega.$ Several equivalent properties characterizing partition analytic spaces are shown, including one of the game theoretic characterizations. The preservation properties of partition analytic spaces are given in this paper.