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Article

Keywords:
functions preserving nowhere dense sets; Baire space
Summary:
A simple machinery is developed for the preservation of Baire spaces under preimages. Subsequently, some properties of maps which preserve nowhere dense sets are given.
References:
[Do] J. Doboš: A note on the invariance of Baire spaces under mappings. Časopis pӗst. matem. 108 (1983), 409-411. MR 0727538
[Du] J. Dugundji: Topology. Wm. C. Bгown Publisheгs, 1989, pp. 256.
[FZ] B. Fitzpatrick, Jr., Zhou Hao-xuan: Countable dense homogeneity and the Baire property. Topology Appl. 4З (1992), 1-4. MR 1141367
[FK] W. G. Fleissner, K. Kunen: Barely Baire spaces. Fund. Math. 101 (1979), 229-240. DOI 10.4064/fm-101-3-229-240 | MR 0521125
[Fr] Z. Frolík: Remarks concerning the invariance of Baire spaces under mappings. Czechoslovak Math. Ј. 11 (1961), 381-385. MR 0133098
[HM] R. C. Haworth, R. A. McCoy: Baire spaces. Dissertationes Math., PWN, Warszawa 141 (1977). MR 0431104 | Zbl 0344.54001
[Ne] T. Neubrunn: A note on mappings of Baire spaces. Math. Slovaca 27 (1977), 173-176. Erratum, ibidem, p. 442. MR 0454910 | Zbl 0371.54023
[No] D. Noll: On the preservation of Baire category under preimages. Proc. Amer. Math. Soc. 107(1989), 847-854. DOI 10.1090/S0002-9939-1989-0982407-2 | MR 0982407 | Zbl 0687.54012
[PR] Z. Piotrowski, I. L. Reilly: Preimages of Baire spaces - an example. Q & A in General Topology 11 (1993), 105-107. MR 1205956 | Zbl 0779.54025
[PS] Z. Piotrowski, A. Szymaśki: Some remarks on category in topological spaces. Proc. Amer. Math. Soc. 101 (1987), 156-160. DOI 10.1090/S0002-9939-1987-0897088-4 | MR 0897088
[Wi] T. E. Wilson: Stгictly irreducible maps and strong transitivity. Topology Proceedings 13 (1988), 371-387. MR 1053705
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