Geodesic
A Note on Small Baire Spaces
Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 659-665

Voir la notice de l'article provenant de la source Cambridge University Press

A Baire space is a topological space which satisfies the Baire Category Theorem, i.e., in which the intersection of countably many dense open sets is dense. In this note we shall be interested in the size of Baire spaces, so to avoid trivialities we shall consider only non-atomic spaces, that is, spaces X whose regular open algebras ro(X) are non-atomic. All natural examples of Baire spaces, such as complete metric spaces or compact spaces, seem to have sizes at least 2א0 . So a natural question, asked first by W. Fleissner and K. Kunen [5], is whether there exists a Baire space of the minimal possible size א1. The purpose of this note is to show that such a space need not exist by proving the following result. 
Shelah, Saharon; Todorcevic, Stevo. A Note on Small Baire Spaces. Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 659-665. doi: 10.4153/CJM-1986-033-8
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