Convergence of sequences of distributions-Reference-Cited by-同舟云学术

Convergence of sequences of distributions

Published:1971 Issue:3 Volume:27 Page:531-534
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Dudley R. M.

Abstract

It is shown that in L. Schwartz’s distribution space D ′ \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 D ′ \mathcal {D}’ .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1971-027-03/S0002-9939-1971-0270145-X/S0002-9939-1971-0270145-X.pdf

Reference9 articles.

1. On sequential convergence;Dudley, R. M.;Trans. Amer. Math. Soc.,1964

2. F. Hausdorff, Gestufte Räume, Fund. Math. 25 (1935), 486-502.

3. Convergence du type \cal𝐿;Kisyński, J.;Colloq. Math.,1959

4. J. Novák, Sur les espaces ((ℒ)) et sur les produits Cartésiens ((ℒ)), Publ. Fac. Sci. Univ. Masaryk No. 273 (1939). MR 1, 221.

5. Publications de l'Institut de Math\'{e}matique de l'Universit\'{e} de Strasbourg, IX-X;Schwartz, Laurent,1966

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. When is a Locally Convex Space Eberlein–Grothendieck?;Results in Mathematics;2022-10-26

2. On Sequential Properties of Spaces of Measures;Mathematical Notes;2021-09

3. Topological properties of strict (LF)-spaces and strong duals of Montel strict (LF)-spaces;Monatshefte für Mathematik;2018-10-20

4. The strong Pytkeev property for topological groups and topological vector spaces;Monatshefte für Mathematik;2014-05-25

5. Über Folgenkonvergenz in lokalkonvexen Räumen;Mathematische Nachrichten;1986