Geodesic
A universal sequence of continuous functions
The Teaching of Mathematics, XIV (2011) no. 2, p. 71

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We show that for each positive integer $k$ there is a sequence $F_n:\Bbb{R}^k \rightarrow\Bbb{R}$ of {t continuous} functions which represents via point-wise limits {t arbitrary} functions $G\:X^k\rightarrow \Bbb{R}$ defined on domains $X\subseteq \Bbb{R}$ of sizes not exceeding a standard cardinal characteristic of the continuum.
Classification : 1AMS03E20 97E60 2ZDME65
Keywords: Point-wise limit, continuum, continuous function. 
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     author = {Stevo Todor\v{c}evi\'c},
     title = {A universal sequence of continuous functions},
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Stevo Todorčević. A universal sequence of continuous functions. The Teaching of Mathematics, XIV (2011) no. 2, p. 71 . http://geodesic.mathdoc.fr/item/TM2_2011_XIV_2_a1/