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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 $$\mathfrak{S}$$ .

Coverings and dimensions in infinite profinite groups

86%

Maga P.

Open Mathematics

2013

tom 11

nr 2

246-253

Answering a question of Miklós Abért, we prove that an infinite profinite group cannot be the union of less than continuum many translates of a compact subset of box dimension less than 1. Furthermore, we show that it is consistent with the axioms of set theory that in any infinite profinite group there exists a compact subset of Hausdorff dimension 0 such that one can cover the group by less than continuum many translates of it.

Ograniczanie wyników

2 Open Mathematics

1 Abel M.

1 Arhippainen J.

1 Kauppi J.

1 Maga P.

1 2013

1 2012

Wyniki wyszukiwania

Description of quotient algebras in function algebras containing continuous unbounded functions

Coverings and dimensions in infinite profinite groups