Preimages d'espaces hereditairement de Baire

摘要

The main result is slightly more general than the following statement: Let / : X —+ Y be a quasi-perfect mapping, where X is a regular space and Y a Hausdorff totally non-meagre space; if X or Y is x-scattered, or if Y is a Lasnev space, then X is totally non-meagre. In particular, the product of a compact space X and a Hausdorff regular totally non-meagre space Y which is x-scattered or a Lasnev space, is totally non-meagre.