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On the preservation of Baire category under preimages


Author: Dominikus Noll
Journal: Proc. Amer. Math. Soc. 107 (1989), 847-854
MSC: Primary 54C10; Secondary 46A30
DOI: https://doi.org/10.1090/S0002-9939-1989-0982407-2
MathSciNet review: 982407
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Abstract: We discuss the problem of preservation of Baire category under continuous and feebly open preimages. We obtain a solution by imposing a completeness condition on the fibres $ {f^{ - 1}}(y)$ of the function $ f$ under consideration. Based on a theorem on the invariance of residuality under continuous and nearly feebly open images, we also derive a result concerning the preservation of category under continuous and nearly feebly open preimages. We end up with an open mapping theorem for functions $ f$ of this kind defined on a Čech complete space.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0982407-2
Keywords: Fibre-completeness, (nearly) feebly open, (nearly) feebly continuous, Čech completeness, open mapping theorem, preimages of Baire spaces
Article copyright: © Copyright 1989 American Mathematical Society

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