Free sequences and the tightness of pseudoradial spaces

Santi Spadaro

doi:10.1007/s13398-020-00861-z

Free sequences and the tightness of pseudoradial spaces

Santi Spadaro

Research output: Contribution to journal › Article › peer-review

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 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 ⁾.

Original language	English
Article number	130
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	114
Issue number	3
DOIs	https://doi.org/10.1007/s13398-020-00861-z
State	Published - 1 Jul 2020
Externally published	Yes

Keywords

Free sequence
Lindelöf degree
Pseudoradial
Radial character
Tightness

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Computational Mathematics
Applied Mathematics

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10.1007/s13398-020-00861-z

Cite this

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abstract = "Let F(X) be the supremum of cardinalities of free sequences in X. We prove that the radial character of every Lindel{\"o}f Hausdorff almost radial space X and the set-tightness of every Lindel{\"o}f Hausdorff space are always bounded above by F(X). We then improve a result of Dow, Juh{\'a}sz, Soukup, Szentmikl{\'o}ssy and Weiss by proving that if X is a Lindel{\"o}f 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 Lindel{\"o}f Hausdorff pseudoradial space then F(Xδ) ≤ 2 F ( X ).",

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AB - 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 ).

KW - Free sequence

KW - Lindelöf degree

KW - Pseudoradial

KW - Radial character

KW - Tightness

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Free sequences and the tightness of pseudoradial spaces

Abstract

Keywords

ASJC Scopus subject areas

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