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). We then improve a result of Dow, Juhász, Soukup, Szentmiklóssy and Weiss by proving that if X is a Lindelöf Hausdorff space, and Xδ denotes the Gδ topology on X then t(Xδ) ≤ 2 t ( X ). Finally, we exploit this to prove that if X is a Lindelöf Hausdorff pseudoradial space then F(Xδ) ≤ 2 F ( X ).
Santi Spadaro (2020). Free sequences and the tightness of pseudoradial spaces. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS, 114(3) [10.1007/s13398-020-00861-z].
Free sequences and the tightness of pseudoradial spaces
Santi Spadaro
2020-01-01
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). We then improve a result of Dow, Juhász, Soukup, Szentmiklóssy and Weiss by proving that if X is a Lindelöf Hausdorff space, and Xδ denotes the Gδ topology on X then t(Xδ) ≤ 2 t ( X ). Finally, we exploit this to prove that if X is a Lindelöf Hausdorff pseudoradial space then F(Xδ) ≤ 2 F ( X ).File | Dimensione | Formato | |
---|---|---|---|
FreepseudoradialRevised3.pdf
Open Access dal 14/05/2021
Tipologia:
Pre-print
Dimensione
258.26 kB
Formato
Adobe PDF
|
258.26 kB | Adobe PDF | Visualizza/Apri |
Spadaro2020_Article_FreeSequencesAndTheTightnessOf (2).pdf
Solo gestori archvio
Descrizione: Articolo completo
Tipologia:
Versione Editoriale
Dimensione
235.61 kB
Formato
Adobe PDF
|
235.61 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.