On the cardinality of the θ-closed hull of sets

被引：5

作者：

Cammaroto, Filippo ^{[1
]}

Catalioto, Andrei ^{[1
]}

Pansera, Bruno Antonio ^{[1
]}

Tsaban, Boaz ^{[2
]}

机构：

[1] Univ Messina, Dipartimento Matemat, I-98166 Messina, Italy

[2] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

来源：

TOPOLOGY AND ITS APPLICATIONS | 2013年 / 160卷 / 18期

关键词：

Urysohn space; n-Urysohn space; Finitely-Urysohn space; Urysohn number; H-closed space; H-set; theta-Closure; theta-Closed hull; theta-Tightness; theta-Bitightness; Finite theta-bitightness; theta-Bitightness small number; theta-Character; Character; Cardinal inequalities; TOPOLOGICAL-SPACE; URYSOHN SPACES; NUMBER;

D O I：

10.1016/j.topol.2013.07.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theta-closed hull of a set A in a topological space is the smallest set C containing A such that, whenever all closed neighborhoods of a point intersect C, this point is in C. We define a new topological cardinal invariant function, the theta-bitightness small number of a space X, bts(0)(X), and prove that in every topological space X, the cardinality of the theta-closed hull of each set A is at most vertical bar A vertical bar(bts theta)(X). Using this result, we synthesize all earlier results on bounds on the cardinality of theta-closed hulls. We provide applications to P-spaces and to the almost-Lindelof number. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：2371 / 2378

页数：8

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