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Topological algebras with maximal regular ideals closed

100%

Abel M.

Open Mathematics

2012

tom 10

nr 3

1054-1059

It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.

Description of quotient algebras in function algebras containing continuous unbounded functions

100%

Abel M., Arhippainen J., Kauppi J.

Open Mathematics

2012

tom 10

nr 3

1060-1066

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 $$\mathfrak{S}$$ .

Ograniczanie wyników

2 Open Mathematics

2 Abel M.

1 Arhippainen J.

1 Kauppi J.

2 2012

Wyniki wyszukiwania

Topological algebras with maximal regular ideals closed

Description of quotient algebras in function algebras containing continuous unbounded functions