Doboš, Jozef; Piotrowski, Z.; Reilly, I. L. Preimages of Baire spaces. (English) Zbl 0815.54010 Math. Bohem. 119, No. 4, 373-379 (1994). 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. Reviewer: R.A.McCoy (Blacksburg) 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 PDF BibTeX XML Cite \textit{J. Doboš} et al., Math. Bohem. 119, No. 4, 373--379 (1994; Zbl 0815.54010) Full Text: EuDML