On closures of discrete sets

被引：0
|
作者：
Spadaro, Santi [1 ]
机构：
[1] Univ Catania, Dept Math & Comp Sci, Citta Univ, Viale A Doria 6, I-95125 Catania, Italy
来源：
QUAESTIONES MATHEMATICAE | 2021年 / 44卷 / 06期
关键词：
Primary; Secondary; Cardinal inequality; Lindelof; discrete set; depth; elementary submodel; SUBSPACES;
D O I：
10.2989/16073606.2019.1617364
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The depth of a topological space X (g(X)) is defined as the supremum of the cardinalities of closures of discrete subsets of X. Solving a problem of Martinez-Ruiz, Ramirez-Paramo and Romero-Morales, we prove that the cardinal inequality |X| <= g(X)(L)((X)) (F)((X)) holds for every Hausdorff space X, where L(X) is the Lindeloof number of X and F (X) is the supremum of the cardinalities of the free sequences in X.
引用
收藏
页码：717 / 720
页数：4
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