Free sequences and the tightness of pseudoradial spaces

2019/12/29 by Santi Spadaro, Spadaro, Santi
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1912.12706

openalex publication_date 2019/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F(X) be the supremum of cardinalities of free sequences in X. We prove that the radial character of every Lindelöf Hausdorff almost radial space X and the set-tightness of every Lindelöf Hausdorff space are always bounded above by F(X). Solving a question of Bella, we exhibit a Hausdorff radial space X whose radial character is strictly larger than F(X). We then improve a result of Dow, Juhász, Soukup, Szentmiklóssy and Weiss by proving that if X is a Lindelöf Hausdorff space, and X_δ denotes the G_δ topology on X then t(X_δ) ≤ 2^t(X). Finally, we exploit this to prove that if X is a Lindelöf Hausdorff pseudoradial space then F(X_δ) ≤ 2^F(X), which partially answer a question of Bella and ourselves.

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