Description of quotient algebras in function algebras containing continuous unbounded functions

• Autorzy: Mati Abel , Jorma Arhippainen , Jukka Kauppi
• Języki publikacji: EN

Abstrakty

EN

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 $$\mathfrak{S}$$ .

Słowa kluczowe

EN

Function algebras; Quotient algebras; Cover; Uniform topology; Strict topology

Kategorie tematyczne

• 46H10: Ideals and subalgebras
• 46H20: Structure, classification of topological algebras
• 46H05: General theory of topological algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1060-1066

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Mati Abel

• University of Tartu

autor

Jorma Arhippainen

• University of Oulu

autor

Jukka Kauppi

• University of Oulu

Bibliografia

• [1] Abel M., Extensions of topological spaces depending on covering, Eesti NSV Tead. Akad. Toimetised Füüs.-Mat., 1981, 30(4), 326–332 (in Russian)
• [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
• [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
• [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
• [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
• [7] Gillman L., Jerison M., Rings of continuous functions, The University Series in Higher Mathematics, Van Nostrand, Princeton-Toronto-London-New York, 1960
• [8] Willard S., General Topology, Addison-Wesley, Reading-London-Don Mills, 1970

Identyfikatory

DOI

10.2478/s11533-012-0043-5