On the preservation of Baire and weakly Baire category

Alireza Kamel Mirmostafaee; Zbigniew Piotrowski

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 4, page 475-481
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Mirmostafaee, Alireza Kamel, and Piotrowski, Zbigniew. "On the preservation of Baire and weakly Baire category." Mathematica Bohemica 141.4 (2016): 475-481. <http://eudml.org/doc/287586>.

@article{Mirmostafaee2016,
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.},
author = {Mirmostafaee, Alireza Kamel, Piotrowski, Zbigniew},
journal = {Mathematica Bohemica},
keywords = {feebly continuous mapping; quasi-interior continuity; Baire space; weakly Baire space; fiber-completeness},
language = {eng},
number = {4},
pages = {475-481},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the preservation of Baire and weakly Baire category},
url = {http://eudml.org/doc/287586},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Mirmostafaee, Alireza Kamel
AU - Piotrowski, Zbigniew
TI - On the preservation of Baire and weakly Baire category
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 4
SP - 475
EP - 481
AB - 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.
LA - eng
KW - feebly continuous mapping; quasi-interior continuity; Baire space; weakly Baire space; fiber-completeness
UR - http://eudml.org/doc/287586
ER -

References

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