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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

When does restricted continuity on continuous function graphs imply joint continuity?


Author: John P. Dalbec
Journal: Proc. Amer. Math. Soc. 118 (1993), 669-674
MSC: Primary 26B05; Secondary 54C05
MathSciNet review: 1129876
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Abstract: We generalize a result of Luzin about real functions of real variables --that $ F(x,y)$ is jointly continuous if and only if $ F(x,f(x))$ is continuous for every continuous $ f$--to functions among certain classes of topological spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1129876-6
PII: S 0002-9939(1993)1129876-6
Article copyright: © Copyright 1993 American Mathematical Society