Hausdorff SDL空间的基数界
Cardinality Bounds for Hausdorff SDL Spaces
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中文总结 AI 辅助
本文针对Hausdorff SDL空间建立基数界不等式，推导得第一可数该类空间基数不超过连续统，解答了Bella与Spadaro的两个问题，还给出SDL空间的一致有界分解性质相关中间结果。
中文摘要 AI 辅助
我们对每个Hausdorff SDL空间X建立基数不等式|X|≤2^{t(X)Hψ(X)}，其中t(X)和Hψ(X)分别表示X的紧度和Hausdorff伪特征。由于这两个不变量均受限于χ(X)，由此可得|X|≤2^{χ(X)}。作为推论，每个第一可数的Hausdorff强细胞林德洛夫空间的基数至多为连续统。这些结果回答了Bella和Spadaro提出的问题2.1和2.2。中间结果是SDL空间的一致有界分解性质；特别地，它们的严格拟林德洛夫数满足⊓L(X)≤t(X)。
英文摘要
We establish the cardinal inequality \(|X|\leq 2^{t(X)Hψ(X)}\) for every Hausdorff SDL space \(X\), where \(t(X)\) and \(Hψ(X)\) denote the tightness and the Hausdorff pseudocharacter of \(X\), respectively. Since both invariants are bounded by \(χ(X)\), this yields \(|X|\leq 2^{χ(X)}\). As a consequence, every first-countable Hausdorff strongly cellular--Lindelöf space has cardinality at most the continuum. These results answer Questions~2.1 and~2.2 of Bella and Spadaro. An intermediate result is a uniform bounded-decomposition property for SDL spaces; in particular, their strict quasi--Lindelöf number satisfies \(\sqL(X)\leq t(X)\).
发表机构
- Institute of Mathematics and Computer Sciences, University of São Paulo（圣保罗大学数学与计算机科学学院）
- Institute of Mathematics and Statistics, University of São Paulo（圣保罗大学数学与统计学院）
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