×

zbMATH — the first resource for mathematics

Pták homomorphism theorem revisited. (English) Zbl 1050.46502
Summary: Rodrigues’ extension of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting states that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open [B. Rodrigues, J. Aust. Math. Soc., Ser. A 47, 322–333 (1989; Zbl 0708.46013)]. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.

MSC:
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] N. Adasch, B. Ernst and D. Keim: Topological Vector Spaces. Lecture Notes in Math. 639. Springer Verlag, 1978. · Zbl 0397.46005
[2] J. Horváth: Locally Convex Spaces. Lecture Notes in Math. 331. Springer-Verlag, 1973.
[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. · Zbl 0708.46013
[5] B. Rodrigues: Some new classes of topological vector spaces with closed graph theorems. Comment. Math. Univ. Carolin. 32 (1991), 287-296. · Zbl 0778.46006
[6] L. M. Sánchez Ruiz: Condiciones de tonelación en espacios vectoriales topológicos. Tesis Doctoral, Universidad de Valencia (1988).
[7] L. M. Sánchez Ruiz: On the Banach-Steinhaus theorem between topological vector spaces and locally convex spaces. Math. Japon. 36 (1991), 143-145. · Zbl 0794.46004
[8] L. M. Sánchez Ruiz: On the closed graph theorem between topological vector spaces and Fréchet spaces. Math. Japon. 36 (1991), 271-275. · Zbl 0746.46007
[9] L. M. Sánchez Ruiz: On completeness and the closed graph theorem. Math. Japon. 36 (1991), 891-894. · Zbl 0746.46009
[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. · Zbl 0913.46002
[11] H. H. Schaefer: Topological Vector Spaces. Springer-Verlag, 1986. · Zbl 0212.14001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.