On certain properties of the spaces of order-preserving functionals

被引：11
|
作者：
Albeverio, S. [2 ,3 ,4 ]
Ayupov, Sh. A. [1 ]
Zaitov, A. A. [1 ]
机构：
[1] Uzbek Acad Sci, Inst Math & Informat Technol, Tashkent 100125, Uzbekistan
[2] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany
[3] BiBoS, SFB 611, Bielefeld, Germany
[4] CERFIM Locarno, Locarno, Switzerland
来源：
TOPOLOGY AND ITS APPLICATIONS | 2008年 / 155卷 / 16期
关键词：
tau-smooth order-preserving functional; Radon order-preserving functional; weight; density; weak density;
D O I：
10.1016/j.topol.2008.05.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper it is proved that the functor O-tau of tau-smooth order preserving functionals and the functor OR of Radon order preserving functionals, do not change the weight of infinite Tychonoff spaces. It is shown that the density and the weak density of infinite Tychonoff spaces do not increase under these functors. Moreover, if X is a metric space with the second axiom of countability then the spaces O-tau (X) and O-R(X) are also metrizable. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：1792 / 1799
页数：8
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