On the preservation of Baire and weakly Baire category

Title:

On the preservation of Baire and weakly Baire category

Creator:

Mirmostafaee, Alireza Kamel and Piotrowski, Zbigniew

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:66ebb73f-2e06-4f37-8ad0-6a8d1e8f1cae
uuid:66ebb73f-2e06-4f37-8ad0-6a8d1e8f1cae
doi:10.21136/MB.2016.0053-15

Subject:

feebly continuous mapping, quasi-interior continuity, Baire space, weakly Baire space, and fiber-completeness

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

475-481

Source:

Mathematica bohemica | 2016 Volume:141 | Number:4

Harvested from:

CDK

Metadata only:

false