SEPARATELY CONTINUOUS FUNCTIONS WITH CLOSED GRAPHS

In this paper we prove that if f: R × R [arrow right] R has a closed graph and all of its x-sections are continuous, and at least one y-section is continuous, then f is continuous. It was already proved by Piotrowski and Wingler [PW] that if f: R × R [arrow right] R has a closed graph and is separat...

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Bibliographic Details
Published inReal analysis exchange Vol. 30; no. 1; pp. 23 - 28
Main Authors Wojcik, Michal Ryszard, Wojcik, Michal Stanislaw
Format Journal Article
LanguageEnglish
Published East Lansing Michigan State University Press 01.01.2004
Subjects
54C05
closed graph
continuity
Mathematical analysis
Mathematical functions
separate continuity
Theorems
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Summary:In this paper we prove that if f: R × R [arrow right] R has a closed graph and all of its x-sections are continuous, and at least one y-section is continuous, then f is continuous. It was already proved by Piotrowski and Wingler [PW] that if f: R × R [arrow right] R has a closed graph and is separately continuous, then f is continuous. Our result is stronger. [PUBLICATION ABSTRACT]
ISSN:0147-1937
1930-1219