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Preimages of Baire spaces. (English) Zbl 0815.54010
The question considered in this paper is: When must the domain of a function that maps onto a Baire space be a Baire space? Some positive results are given using the concept of a nowhere-dense-set preserving (nd-preserving) function. For example, if there is a feebly open nd- preserving function mapping $$X$$ onto a Baire space, then $$X$$ is a Baire space. A number of examples are used to illustrate how the nd-preserving property relates to other properties of functions.
##### MSC:
 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54C05 Continuous maps 54E52 Baire category, Baire spaces
##### Keywords:
functions preserving nowhere dense sets; Baire space
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