Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.40

Retrieve articles in all journals with MSC: 46.40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0270145-X
PII: S 0002-9939(1971)0270145-X
Keywords: Sequential topology, sequentially closed set, topological vector space, Schwartz distributions
Article copyright: © Copyright 1971 American Mathematical Society