More on closed non-vanishing ideals in CB(X)

  • 1 Department of Mathematical Sciences, Isfahan University of Technology, 84156–83111, Isfahan, Iran
Amin Khademi
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  • Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156–83111, Iran
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Abstract

Let X be a completely regular topological space. For each closed non-vanishing ideal H of CB(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 𝔰𝔭(H). We make a correspondence between algebraic properties of H and topological properties of 𝔰𝔭(H). This continues some previous studies, in which topological properties of 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 𝔰𝔭(H) such as weak paracompactness, sequential compactness and pseudocompactness. We also study the ideal isomorphisms between two non-vanishing closed ideals of CB(X).

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Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process.

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