Geodesic
On the preservation of Baire and weakly Baire category
Mathematica Bohemica, Tome 141 (2016) no. 4, pp. 475-481
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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.
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.
DOI : 10.21136/MB.2016.0053-15
Classification : 54C10, 54E52
Keywords: feebly continuous mapping; quasi-interior continuity; Baire space; weakly Baire space; fiber-completeness 
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Mirmostafaee, Alireza Kamel; Piotrowski, Zbigniew. On the preservation of Baire and weakly Baire category. Mathematica Bohemica, Tome 141 (2016) no. 4, pp. 475-481. doi: 10.21136/MB.2016.0053-15

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