On strongly separately continuous functions on sequence spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:439

Article

Karlova, Olena¹  Visnyai, Tomas² 

[1] Chernivtsi Natl Univ, Fac Math & Informat, Dept Math Anal, Kotsyubynskoho 2, UA-58012 Chernovtsy, Ukraine

[2] Slovak Univ Technol Bratislava, Fac Chem & Food Technol, Inst Informat Engn Automat & Math, Radlinskeho 9, Bratislava 81237, Slovakia

关键词: Strongly separately continuous function;    Determining set;    Baire classification;   

DOI  :  10.1016/j.jmaa.2016.02.064

来源: Elsevier

【 摘 要 】

We study strongly separately continuous real-valued function defined on the Banach spaces ep. Determining sets for the class of strongly separately continuous functions on 4 are characterized. We prove that for every 2 < alpha < col there exists a strongly separately continuous function which belongs to the a'th Baire class and does not belong to the /Yth Baire class on ep for fi < a. We show that any open set in ep is the set of discontinuities of a strongly separately continuous real-valued function. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free