Mazur-like topological linear spaces and their products
Hušek, Miroslav
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 157-164 / Harvested from Czech Digital Mathematics Library

Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.

Publié le : 1997-01-01
Classification:  22A99,  46A03,  54B10,  54C08,  54H11
@article{118911,
     author = {Miroslav Hu\v sek},
     title = {Mazur-like topological linear spaces and their products},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {157-164},
     zbl = {0886.46005},
     mrnumber = {1455479},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118911}
}
Hušek, Miroslav. Mazur-like topological linear spaces and their products. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 157-164. http://gdmltest.u-ga.fr/item/118911/

Adámek J.; Herrlich H.; Strecker G. Abstract and Concrete Categories, Wiley Interscience, New York, 1990. | MR 1051419

Dierolf P.; Dierolf S. On linear topologies determined by a family of subsets of a topological vector spaces, Gen. Top. and its Appl. 8 (1978), 127-140. (1978) | MR 0473867

Dudley R.M. On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483-507. (1964) | MR 0175081 | Zbl 0138.17401

Engelking R. General Topology, Heldermann Verlag, Berlin, 1989. | MR 1039321 | Zbl 0684.54001

Hušek M. Sequentially continuous homomorphisms on products of topological groups, Top. & Appl. 70 (1996), 155-165. (1996) | MR 1397074

Isbell J.R. Mazur's theorem, Proc. Top. Symp. Prague 1961 (Academia Prague 1962), pp.221-225. | MR 0146640 | Zbl 0116.31803

Isbell J.R.; Thomas E.S., Jr. Mazur's theorem on sequentially continuous linear functionals, Proc. Amer. Math. Soc. 14 (1963), 644-647. (1963) | MR 0151833 | Zbl 0116.31803

Jarchow H. Locally Convex Spaces, Teubner, Stuttgart, 1981. | MR 0632257 | Zbl 0466.46001

Mazur S. Sur la structure des fonctionelles linéaires dans certains espaces $(\Cal L)$, Ann. Soc. Polon. Math. 19 (1946), 241. (1946)

Mazur S. On continuous mappings on cartesian products, Fund. Math. 39 (1952), 229-238. (1952) | MR 0055663

Mrówka S. On the form of certain functionals, Bull. Acad. Polon. Sci. Ser. Math. 5 (1957), 1061-1067. (1957) | MR 0092111

Mrówka S. On the form of pointwise continuous linear positive functionals and isomorphisms of function spaces, Studia Math. 21 (1961), 1-14. (1961) | MR 0138992

Snipes R.F. C-sequential and S-bornological spaces, Math. Ann. 202 (1973), 273-283. (1973) | MR 0330993

Sydow W. Über die Kategorie der topologischen Vektorräume, Doktor-Dissertation (Fernuniversität Hagen, 1980). | Zbl 0466.18006

Wilansky A. Modern Methods in Topological Vector Spaces, McGraw-Hill, 1978. | MR 0518316 | Zbl 0395.46001