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On the preservation of Baire category under preimages. (English) Zbl 0687.54012
Summary: 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.

MSC:
 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54E52 Baire category, Baire spaces 46A30 Open mapping and closed graph theorems; completeness (including $$B$$-, $$B_r$$-completeness)
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References:
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