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 in:	Topology and its applications Vol. 160; no. 12; pp. 1439 - 1443
Main Authors:	Bielas, Wojciech, Miller, Arnold W., Morayne, Michał, Słonka, Tomasz
Format:	Journal Article
Language:	English
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
Online Access:	Get full text
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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