More on closed non-vanishing ideals in $C_B(X)$

Year, pages: 2020, 909 - 916

Let $X$ be a completely regular topological space. For each closed non-vanishing ideal $H$ of $C_B(X)$, the normed algebra of all bounded continuous scalar-valued mappings on $X$ equipped with pointwise addition and multiplication and the supremum norm, we study its spectrum, denoted by $\mathfrak{sp}(H)$. We make a correspondence between algebraic properties of $H$ and topological properties of $\mathfrak{sp}(H)$. This continues some previous studies, in which topological properties of $\mathfrak{sp}(H)$ such as the Lindelöf property, paracompactness, $σ$-compactness and countable compactness have been made into correspondence with algebraic properties of $H$. We study here other compactness properties of $\mathfrak{sp}(H)$ such as weak paracompactness, sequential compactness and pseudocompactness. We also study the ideal isomorphisms between two non-vanishing closed ideals of $C_B(X)$.

Khademi, A. 2020. More on closed non-vanishing ideals in $C_B(X)$. In Mathematica Slovaca, vol. 70, no.4, pp. 909-916. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0403

Khademi, A. (2020). More on closed non-vanishing ideals in $C_B(X)$. Mathematica Slovaca, 70(4), 909-916. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0403

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava