Mathematica Bohemica, Vol. 141, No. 4, pp. 475-481, 2016
On the preservation of Baire and weakly Baire category
Alireza Kamel Mirmostafaee, Zbigniew Piotrowski
Received September 13, 2015. First published September 12, 2016.
Abstract: We consider the question of preservation of Baire and weakly Baire category under images and preimages of certain kind of functions. It is known that Baire category is preserved under image of quasi-continuous feebly open surjections. In order to extend this result, we introduce a strictly larger class of quasi-continuous functions, i.e. the class of quasi-interior continuous functions. We show that Baire and weakly Baire categories are preserved under image of feebly open quasi-interior continuous surjections. We also give a new definition for countably fiber-completeness of a function. We prove that Baire category is preserved under inverse image of a countably fiber-complete function provided that it is feebly open and feebly continuous.
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Affiliations: Alireza Kamel Mirmostafaee, Center of Excellence in Analysis on Algebraic Structures, Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Azadi Sq., Mashhad 91775, Iran, e-mail: mirmostafaei@um.ac.ir; Zbigniew Piotrowski, Department of Mathematics and Statistics, Youngstown State University, Lincoln Building Office 518, One University Plaza, Youngstown, Ohio, 44555, USA, e-mail: zpiotr@as.ysu.edu
