<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We prove that the family Q of quasi-continuous functions is a strongly porous set in the space Ba of functions having the Baire property. Moreover, the family DQ of all Darboux quasi-continuous functions is a strongly porous set in the space DBa of Darboux functions having the Baire property. It implies that each family of all functions having the A-Darboux property is strongly porous in DBa if A has the (∗)-property.</p></abstract>

We prove that the family Q of quasi-continuous functions is a strongly porous set in the space Ba of functions having the Baire property. Moreover, the family DQ of all Darboux quasi-continuous functions is a strongly porous set in the space DBa of Darboux functions having the Baire property. It implies that each family of all functions having the A-Darboux property is strongly porous in DBa if A has the (∗)-property.

Comparison of Some Subfamilies of Functions Having The Baire Property

Institute of Mathematics Academia Pomeraniensis ul. Arciszewskiego 22d PL–76-200 Słupsk POLAND

University of Łódź Faculty of Mathematics and Computer Science ul. Banacha 22 PL–90-238 Łódź POLAND

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Comparison of Some Subfamilies of Functions Having The Baire Property"}

We prove that the family Q of quasi-continuous functions is a strongly porous set in the space Ba of functions having the Baire property. Moreover, the family...

Comparison of Some Subfamilies of Functions Having The Baire Property

Publié en ligne: 04 août 2016

Pages: 151 - 159

Reçu: 19 nov. 2015

DOI: https://doi.org/10.1515/tmmp-2016-0013

Mots clés
Darboux property, Baire property, quasi-continuous functions, porous set

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Comparison of Some Subfamilies of Functions Having The Baire Property

Publié en ligne: 04 août 2016

Pages: 151 - 159

Reçu: 19 nov. 2015

DOI: https://doi.org/10.1515/tmmp-2016-0013

Mots clésDarboux property, Baire property, quasi-continuous functions, porous set

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Darboux property, Baire property, quasi-continuous functions, porous set