Abstract
We study spaces that can be mapped onto the Baire space (i.e. the countable power of the countable discrete space) by a continuous quasi-open bijection. We give a characterization of such spaces in terms of Souslin schemes and call these spaces π-spaces. We show that every space that has a Lusin π-base is a π-space and that every second-countable π-space has a Lusin π-base. The main result of this paper is a characterization of continuous open images of π-space.
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