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ArticleOriginal scientific text

Title

Complexity of the class of Peano functions

Authors ¹, ², ³

Affiliations

Institute of Mathematics, University of Wrocław, 50-384 Wrocław, Poland
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
Department of Mathematics, Washington University, St. Louis, MO 63130, U.S.A.

Abstract

We evaluate the descriptive set theoretic complexity of the space of continuous surjections from

ℝ^{m}

to

ℝ^{n}

.

J. J. Charatonik and T. Maćkowiak, Around Effros' theorem, Trans. Amer. Math. Soc. 298 (1986), 579-602.
E. G. Effros, Transformation groups and C*-algebras, Ann. of Math. 81 (1965), 38-55.
A. S. Kechris, On the concept of $Π^{1}_1$ -completeness, Proc. Amer. Math. Soc. 125 (1997), 1811-1814.
A. S. Kechris, Classical Descriptive Set Theory, Springer, 1995.
P. Krupski, Homogeneity and Cantor manifolds, Proc. Amer. Math. Soc. 109 (1990), 1135-1142.