Generating Borel measurable mappings with continuous mappings

被引：0

作者：

Bielas, Wojciech ^{[1
]}

Miller, Arnold W. ^{[2
]}

Morayne, Michal ^{[3
]}

Slonka, Tomasz ^{[1
]}

机构：

[1] Univ Silesia, Inst Math, PL-40007 Katowice, Poland

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[3] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

来源：

TOPOLOGY AND ITS APPLICATIONS | 2013年 / 160卷 / 12期

关键词：

Semigroup; Relative rank; Borel measurable mapping; Continuous mapping;

D O I：

10.1016/j.topol.2013.05.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the relative rank r(B(X):C(X)) of the semigroup of Borel mappings B(X) from X to X (with the composition of mappings as the semigroup operation) with respect to the semigroup of continuous functions C(X) from X to X is equal to N-1 if X is an uncountable Polish space which either can be retracted to a Cantor subset of X, or contains an arc, or is homeomorphic to its Cartesian square X-2. (C) 2013 Elsevier B.V. All rights reserved.

引用

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页码：1439 / 1443

页数：5

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