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arXiv · 2609.00599

Cardinality Bounds for Hausdorff SDL Spaces

Gabriel Fernandes·João Marcelo Maciel Messias
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Abstract

We establish the cardinal inequality \(|X|\leq 2^{t(X)H\psi(X)}\) for every Hausdorff SDL space \(X\), where \(t(X)\) and \(H\psi(X)\) denote the tightness and the Hausdorff pseudocharacter of \(X\), respectively. Since both invariants are bounded by \(\chi(X)\), this yields \(|X|\leq 2^{\chi(X)}\). As a consequence, every first-countable Hausdorff strongly cellular--Lindel\"of 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--Lindel\"of number satisfies \(\sqL(X)\leq t(X)\).

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Gabriel Fernandes, João Marcelo Maciel Messias. 2026-09-01. Cardinality Bounds for Hausdorff SDL Spaces. https://arxiv.org/abs/2609.00599

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