Previous |  Up |  Next


homomorphism theorem B-complete space; B-complete space
Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.
[1] N. Adasch, B. Ernst and D. Keim: Topological Vector Spaces. Lecture Notes in Math. 639. Springer Verlag, 1978. MR 0487376
[2] J. Horváth: Locally Convex Spaces. Lecture Notes in Math. 331. Springer-Verlag, 1973. MR 0482027
[3] G. Köthe: Topological Vector Spaces. Springer-Verlag, 1969.
[4] B. Rodrigues: On Pták homomorphism theorem. J. Austral. Math. Soc. Ser. A 47 (1989), 322–333. DOI 10.1017/S144678870003175X | MR 1008846
[5] B. Rodrigues: Some new classes of topological vector spaces with closed graph theorems. Comment. Math. Univ. Carolin. 32 (1991), 287–296. MR 1137790 | Zbl 0778.46006
[6] L. M. Sánchez Ruiz: Condiciones de tonelación en espacios vectoriales topológicos. Tesis Doctoral, Universidad de Valencia (1988). MR 2714480
[7] L. M. Sánchez Ruiz: On the Banach-Steinhaus theorem between topological vector spaces and locally convex spaces. Math. Japon. 36 (1991), 143–145. MR 1093364
[8] L. M. Sánchez Ruiz: On the closed graph theorem between topological vector spaces and Fréchet spaces. Math. Japon. 36 (1991), 271–275. MR 1095740
[9] L. M. Sánchez Ruiz: On completeness and the closed graph theorem. Math. Japon. 36 (1991), 891–894. MR 1128440
[10] L. M. Sánchez Ruiz: Topological Vector Spaces Without Local Convexity Conditions. Functional Analysis with Current Applications in Science, Technology and Industry, M. Brokate and A. H. Siddiqi, Editors. Pitman RNMS, Longman, 1998, pp. 37–48. MR 1607876
[11] H. H. Schaefer: Topological Vector Spaces. Springer-Verlag, 1986. MR 0342978
Partner of
EuDML logo