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Free sequences and the tightness of pseudoradial spaces
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2020-05-13 , DOI: 10.1007/s13398-020-00861-z
Santi Spadaro

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 $$X_\delta $$ X δ denotes the $$G_\delta $$ G δ topology on X then $$t(X_\delta ) \le 2^{t(X)}$$ t ( X δ ) ≤ 2 t ( X ) . Finally, we exploit this to prove that if X is a Lindelöf Hausdorff pseudoradial space then $$F(X_\delta ) \le 2^{F(X)}$$ F ( X δ ) ≤ 2 F ( X ) .

中文翻译:

自由序列和伪径向空间的紧密度

令 F ( X ) 是 X 中自由序列的基数的上位。我们证明了每个 Lindelöf Hausdorff 几乎径向空间 X 的径向特征和每个 Lindelöf Hausdorff 空间的紧度总是由 F ( X ) 上界。然后我们改进了 Dow、Juhász、Soukup、Szentmiklóssy 和 Weiss 的结果,证明如果 X 是 Lindelöf Hausdorff 空间,并且 $$X_\delta $$ X δ 表示 X 上的 $$G_\delta $$ G δ 拓扑然后 $$t(X_\delta ) \le 2^{t(X)}$$ t ( X δ ) ≤ 2 t ( X ) 。最后,我们利用这一点来证明如果 X 是 Lindelöf Hausdorff 伪径向空间,则 $$F(X_\delta ) \le 2^{F(X)}$$ F ( X δ ) ≤ 2 F ( X ) 。
更新日期:2020-05-13
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