Strict topologies as topological algebras

Surjit Singh Khurana

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 2, page 433-437
  • ISSN: 0011-4642

Abstract

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Let X be a completely regular Hausdorff space, C b ( X ) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m -convex.

How to cite

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Khurana, Surjit Singh. "Strict topologies as topological algebras." Czechoslovak Mathematical Journal 51.2 (2001): 433-437. <http://eudml.org/doc/30645>.

@article{Khurana2001,
abstract = {Let $X$ be a completely regular Hausdorff space, $C_\{b\}(X)$ the space of all scalar-valued bounded continuous functions on $X$ with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally $m$-convex.},
author = {Khurana, Surjit Singh},
journal = {Czechoslovak Mathematical Journal},
keywords = {strict topologies; locally convex algebras; locally $m$-convex algebras; strict topologies; locally convex algebras; locally -convex algebras; completely regular Hausdorff space},
language = {eng},
number = {2},
pages = {433-437},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Strict topologies as topological algebras},
url = {http://eudml.org/doc/30645},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Khurana, Surjit Singh
TI - Strict topologies as topological algebras
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 433
EP - 437
AB - Let $X$ be a completely regular Hausdorff space, $C_{b}(X)$ the space of all scalar-valued bounded continuous functions on $X$ with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally $m$-convex.
LA - eng
KW - strict topologies; locally convex algebras; locally $m$-convex algebras; strict topologies; locally convex algebras; locally -convex algebras; completely regular Hausdorff space
UR - http://eudml.org/doc/30645
ER -

References

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  11. 10.1090/S0002-9947-1972-0295065-1, Trans. Amer. Math. Soc. 168 (1972), 311–336. (1972) MR0295065DOI10.1090/S0002-9947-1972-0295065-1
  12. Une caracterisation des espaces universellement Radon measurables, C.  R.  Acad. Sci. Paris 268 (1969), 864–866. (1969) MR0248321
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