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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更多关于 CB(X) 中的闭非零理想

摘要 设 X 是一个完全正则的拓扑空间。对于CB(X)的每个封闭非消失理想H，X上所有带点加法和乘法的有界连续标量值映射的赋范代数，以及最高范数，我们研究它的频谱，用𝔰𝔭(H)表示。我们将H的代数性质和𝔰𝔭(H)的拓扑性质对应起来。这延续了之前的一些研究，其中 𝔰𝔭(H) 的拓扑性质，例如 Lindelöf 性质、副紧性、σ-紧性和可数紧致性已与 H 的代数性质对应。我们在这里研究𝔰𝔭(H) 的其他紧致性性质)，例如弱副紧性、顺序紧致性和伪紧致性。我们还研究了 CB(X) 的两个非零闭理想之间的理想同构。