# Description of quotient algebras in function algebras containing continuous unbounded functions

Mati Abel; Jorma Arhippainen; Jukka Kauppi

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 1060-1066
- ISSN: 2391-5455

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topMati Abel, Jorma Arhippainen, and Jukka Kauppi. "Description of quotient algebras in function algebras containing continuous unbounded functions." Open Mathematics 10.3 (2012): 1060-1066. <http://eudml.org/doc/269330>.

@article{MatiAbel2012,

abstract = {Let X be a completely regular Hausdorff space, \[\mathfrak \{S\}\]
a cover of X, and \[C\_b (X,\mathbb \{K\};\mathfrak \{S\})\]
the algebra of all \[\mathbb \{K\}\]
-valued continuous functions on X which are bounded on every \[S \in \mathfrak \{S\}\]
. A description of quotient algebras of \[C\_b (X,\mathbb \{K\};\mathfrak \{S\})\]
is given with respect to the topologies of uniform and strict convergence on the elements of \[\mathfrak \{S\}\]
.},

author = {Mati Abel, Jorma Arhippainen, Jukka Kauppi},

journal = {Open Mathematics},

keywords = {Function algebras; Quotient algebras; Cover; Uniform topology; Strict topology; function algebras; quotient algebras; cover; uniform topology; strict topology},

language = {eng},

number = {3},

pages = {1060-1066},

title = {Description of quotient algebras in function algebras containing continuous unbounded functions},

url = {http://eudml.org/doc/269330},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Mati Abel

AU - Jorma Arhippainen

AU - Jukka Kauppi

TI - Description of quotient algebras in function algebras containing continuous unbounded functions

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 1060

EP - 1066

AB - Let X be a completely regular Hausdorff space, \[\mathfrak {S}\]
a cover of X, and \[C_b (X,\mathbb {K};\mathfrak {S})\]
the algebra of all \[\mathbb {K}\]
-valued continuous functions on X which are bounded on every \[S \in \mathfrak {S}\]
. A description of quotient algebras of \[C_b (X,\mathbb {K};\mathfrak {S})\]
is given with respect to the topologies of uniform and strict convergence on the elements of \[\mathfrak {S}\]
.

LA - eng

KW - Function algebras; Quotient algebras; Cover; Uniform topology; Strict topology; function algebras; quotient algebras; cover; uniform topology; strict topology

UR - http://eudml.org/doc/269330

ER -

## References

top- [1] Abel M., Extensions of topological spaces depending on covering, Eesti NSV Tead. Akad. Toimetised Füüs.-Mat., 1981, 30(4), 326–332 (in Russian) Zbl0478.54020
- [2] Abel M., The extensions of topological spaces depending on cover and its applications, In: General Topology and its Relations to Modern Analysis and Algebra, 5, The Fifth Prague Topological Symposium, Prague, August 24–28, 1981, Sigma Ser. Pure Math., 3, Heldermann, Berlin, 1983, 6–8
- [3] Abel M., Arhippainen J., Kauppi J., Stone-Weierstrass type theorems for algebras containing continuous unbounded functions, Sci. Math. Jpn., 2010, 71(1), 1–10 Zbl1198.46025
- [4] Abel M., Arhippainen J., Kauppi J., Description of closed ideals in function algebras containing continuous unbounded functions, Mediterr. J. Math., 2010, 7(3), 271–282 http://dx.doi.org/10.1007/s00009-010-0035-2 Zbl1211.46055
- [5] Arhippainen J., On locally A-convex function algebras, In: General Topological Algebras, Tartu, October 4–7, 1999, Math. Stud. (Tartu), Est. Math. Soc. Tartu, 1, Estonian Mathematical Society, Tartu, 2001, 37–41 Zbl1029.46067
- [6] Arhippainen J., Kauppi J., Generalization of the topological algebra (C b(X); β), Studia Math., 2009, 191(3), 247–262 http://dx.doi.org/10.4064/sm191-3-6 Zbl1176.46050
- [7] Gillman L., Jerison M., Rings of continuous functions, The University Series in Higher Mathematics, Van Nostrand, Princeton-Toronto-London-New York, 1960 Zbl0093.30001
- [8] Willard S., General Topology, Addison-Wesley, Reading-London-Don Mills, 1970

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