Debs, Gabriel Parametrisations boréliennes. (Borel parametrization). (French) Zbl 0589.28004 Proc. Am. Math. Soc. 94, 675-681 (1985). It is well known that any dense in itself Polish space X can be obtained as a one-to-one continuous image of the set J of the irrationals by some mapping f. Moreover, if X is zero dimensional then one can construct f such that it is a homeomorphism from J onto X. In this paper we study the Borel complexity of these constructions. MSC: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 03E15 Descriptive set theory Keywords:Borel set; uniformization; Polish space; Borel complexity PDFBibTeX XMLCite \textit{G. Debs}, Proc. Am. Math. Soc. 94, 675--681 (1985; Zbl 0589.28004) Full Text: DOI