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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convergence of sequences of distributions


Author: R. M. Dudley
Journal: Proc. Amer. Math. Soc. 27 (1971), 531-534
MSC: Primary 46.40
MathSciNet review: 0270145
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Abstract: It is shown that in L. Schwartz's distribution space $ \mathcal{D}'$, there exist sequentially open sets which are not open. The class of all sequentially open sets is not compatible with the vector space structure on $ \mathcal{D}'$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0270145-X
Keywords: Sequential topology, sequentially closed set, topological vector space, Schwartz distributions
Article copyright: © Copyright 1971 American Mathematical Society