Convergence of sequences of distributions

Dudley, R. M.

doi:10.1090/S0002-9939-1971-0270145-X

Convergence of sequences of distributions
HTML articles powered by AMS MathViewer

by R. M. Dudley PDF

Proc. Amer. Math. Soc. 27 (1971), 531-534 Request permission

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

R. M. Dudley, On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483–507. MR 175081, DOI 10.1090/S0002-9947-1964-0175081-6

Gestufte Räume

25

J. Kisyński, Convergence du type ${\cal L}$, Colloq. Math. 7 (1959/60), 205–211 (French). MR 123287, DOI 10.4064/cm-7-2-205-211

Sur les espaces ($(\mathcal {L})$) et sur les produits Cartésiens ($(\mathcal {L})$)

1

Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
Tameharu Shirai, Sur les topologies des espaces de L. Schwartz, Proc. Japan Acad. 35 (1959), 31–36 (French). MR 105613
W. Słowikowski, Extensions of sequentially continuous linear functionals in inductive sequences of $({\cal F})$-spaces, Studia Math. 26 (1966), 193–221. MR 192322, DOI 10.4064/sm-26-2-193-221
Raimond A. Struble, A genuine topology for the field of Mikusiński operators, Canad. Math. Bull. 11 (1968), 297–299. MR 233200, DOI 10.4153/CMB-1968-038-8
J. H. Webb, Sequential convergence in locally convex spaces, Proc. Cambridge Philos. Soc. 64 (1968), 341–364. MR 222602, DOI 10.1017/s0305004100042900