Mazur-like topological linear spaces and their products

Miroslav Hušek

Commentationes Mathematicae Universitatis Carolinae (1997)

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

Abstract

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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.

How to cite

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Hušek, 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

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  10. Mazur S., On continuous mappings on cartesian products, Fund. Math. 39 (1952), 229-238. (1952) MR0055663
  11. Mrówka S., On the form of certain functionals, Bull. Acad. Polon. Sci. Ser. Math. 5 (1957), 1061-1067. (1957) MR0092111
  12. Mrówka S., On the form of pointwise continuous linear positive functionals and isomorphisms of function spaces, Studia Math. 21 (1961), 1-14. (1961) MR0138992
  13. Snipes R.F., C-sequential and S-bornological spaces, Math. Ann. 202 (1973), 273-283. (1973) MR0330993
  14. Sydow W., Über die Kategorie der topologischen Vektorräume, Doktor-Dissertation (Fernuniversität Hagen, 1980). Zbl0466.18006
  15. Wilansky A., Modern Methods in Topological Vector Spaces, McGraw-Hill, 1978. Zbl0395.46001MR0518316

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