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Convergence of sequences of distributions


Author: R. M. Dudley
Journal: Proc. Amer. Math. Soc. 27 (1971), 531-534
MSC: Primary 46.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0270145-X
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}'$.


References [Enhancements On Off] (What's this?)

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Additional Information

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

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