Dichotomies for ${\bf C}_0(X)$ and ${\bf C}_b(X)$ spaces

Title:

Dichotomies for ${\bf C}_0(X)$ and ${\bf C}_b(X)$ spaces

Creator:

Glab, Szymon and Strobin, Filip

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:184d0e0d-7d7b-481d-871b-affee3d660dc
uuid:184d0e0d-7d7b-481d-871b-affee3d660dc

Subject:

continuous function, integration, Baire category, and porosity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Jachymski showed that the set $$ \bigg \{(x,y)\in {\bf c}_0\times {\bf c}_0\colon \bigg (\sum _{i=1}^n \alpha (i)x(i)y(i)\bigg )_{n=1}^\infty \text {is bounded}\bigg \} $$ is either a meager subset of ${\bf c}_0\times {\bf c}_0$ or is equal to ${\bf c}_0\times {\bf c}_0$. In the paper we generalize this result by considering more general spaces than ${\bf c}_0$, namely ${\bf C}_0(X)$, the space of all continuous functions which vanish at infinity, and ${\bf C}_b(X)$, the space of all continuous bounded functions. Moreover, we replace the meagerness by $\sigma $-porosity.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

91-105

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:1

Harvested from:

CDK

Metadata only:

false