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

A local kernel property of closed derivations on $ C(I\times I)$


Author: Katsuyoshi Nishio
Journal: Proc. Amer. Math. Soc. 95 (1985), 573-576
MSC: Primary 46J05; Secondary 46L05, 46L40
MathSciNet review: 810166
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Abstract: In this note we show a local behavior of closed derivations on $ C\left( {\left[ {0,1} \right] \times \left[ {0,1} \right]} \right)$, which is essentially different from one-dimensional derivations. Roughly speaking, any closed derivations on $ C\left( {\left[ {0,1} \right] \times \left[ {0,1} \right]} \right)$ has a nonconstant kernel locally.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0810166-9
PII: S 0002-9939(1985)0810166-9
Keywords: Derivation, closed operator, continuous function
Article copyright: © Copyright 1985 American Mathematical Society