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Title: On the preservation of Baire and weakly Baire category (English)
Author: Mirmostafaee, Alireza Kamel
Author: Piotrowski, Zbigniew
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 141
Issue: 4
Year: 2016
Pages: 475-481
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: feebly continuous mapping
Keyword: quasi-interior continuity
Keyword: Baire space
Keyword: weakly Baire space
Keyword: fiber-completeness
MSC: 54C10
MSC: 54E52
idZBL: Zbl 06674857
idMR: MR3576794
DOI: 10.21136/MB.2016.0053-15
Date available: 2017-01-03T15:16:29Z
Last updated: 2020-07-01
Stable URL:
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