# Mazur-like topological linear spaces and their products

Commentationes Mathematicae Universitatis Carolinae (1997)

- Volume: 38, Issue: 1, page 157-164
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top## How to cite

topHušek, Miroslav. "Mazur-like topological linear spaces and their products." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 157-164. <http://eudml.org/doc/248075>.

@article{Hušek1997,

abstract = {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.},

author = {Hušek, Miroslav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {sequentially continuous linear map; topological linear space; product space; sequentially continuous linear map; topological linear space; product space},

language = {eng},

number = {1},

pages = {157-164},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Mazur-like topological linear spaces and their products},

url = {http://eudml.org/doc/248075},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Hušek, Miroslav

TI - Mazur-like topological linear spaces and their products

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1997

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 38

IS - 1

SP - 157

EP - 164

AB - 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.

LA - eng

KW - sequentially continuous linear map; topological linear space; product space; sequentially continuous linear map; topological linear space; product space

UR - http://eudml.org/doc/248075

ER -

## References

top- Adámek J., Herrlich H., Strecker G., Abstract and Concrete Categories, Wiley Interscience, New York, 1990. MR1051419
- 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) MR0473867
- Dudley R.M., On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483-507. (1964) Zbl0138.17401MR0175081
- Engelking R., General Topology, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
- Hušek M., Sequentially continuous homomorphisms on products of topological groups, Top. & Appl. 70 (1996), 155-165. (1996) MR1397074
- Isbell J.R., Mazur's theorem, Proc. Top. Symp. Prague 1961 (Academia Prague 1962), pp.221-225. Zbl0116.31803MR0146640
- Isbell J.R., Thomas E.S., Jr., Mazur's theorem on sequentially continuous linear functionals, Proc. Amer. Math. Soc. 14 (1963), 644-647. (1963) Zbl0116.31803MR0151833
- Jarchow H., Locally Convex Spaces, Teubner, Stuttgart, 1981. Zbl0466.46001MR0632257
- Mazur S., Sur la structure des fonctionelles linéaires dans certains espaces $\left(\mathcal{L}\right)$, Ann. Soc. Polon. Math. 19 (1946), 241. (1946)
- Mazur S., On continuous mappings on cartesian products, Fund. Math. 39 (1952), 229-238. (1952) MR0055663
- Mrówka S., On the form of certain functionals, Bull. Acad. Polon. Sci. Ser. Math. 5 (1957), 1061-1067. (1957) MR0092111
- Mrówka S., On the form of pointwise continuous linear positive functionals and isomorphisms of function spaces, Studia Math. 21 (1961), 1-14. (1961) MR0138992
- Snipes R.F., C-sequential and S-bornological spaces, Math. Ann. 202 (1973), 273-283. (1973) MR0330993
- Sydow W., Über die Kategorie der topologischen Vektorräume, Doktor-Dissertation (Fernuniversität Hagen, 1980). Zbl0466.18006
- Wilansky A., Modern Methods in Topological Vector Spaces, McGraw-Hill, 1978. Zbl0395.46001MR0518316

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.