Generating Borel measurable mappings with continuous mappings

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 ℵ1 if X is an uncountable Polish space which either can be...

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Bibliographic Details
Published inTopology and its applications Vol. 160; no. 12; pp. 1439 - 1443
Main Authors Bielas, Wojciech, Miller, Arnold W., Morayne, Michał, Słonka, Tomasz
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2013
Subjects
Borel measurable mapping
Continuous mapping
Relative rank
Semigroup
Continuous mapping
20M20
Semigroup
Borel measurable mapping
Relative rank
54H15
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Summary: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 ℵ1 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 X2.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2013.05.019