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- W4287979086 abstract "Let $F(X)$ be the supremum of cardinalities of free sequences in $X$. We prove that the radial character of every Lindelof Hausdorff almost radial space $X$ and the set-tightness of every Lindelof 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, Juh'asz, Soukup, Szentmikl'ossy and Weiss by proving that if $X$ is a Lindelof Hausdorff space, and $X_delta$ denotes the $G_delta$ topology on $X$ then $t(X_delta) leq 2^{t(X)}$. Finally, we exploit this to prove that if $X$ is a Lindelof Hausdorff pseudoradial space then $F(X_delta) leq 2^{F(X)}$, which partially answer a question of Bella and ourselves." @default.
- W4287979086 created "2022-07-26" @default.
- W4287979086 creator A5083690716 @default.
- W4287979086 date "2019-12-29" @default.
- W4287979086 modified "2023-09-28" @default.
- W4287979086 title "Free sequences and the tightness of pseudoradial spaces" @default.
- W4287979086 doi "https://doi.org/10.48550/arxiv.1912.12706" @default.
- W4287979086 hasPublicationYear "2019" @default.
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