Geodesic
On the Quasinormal Convergence of Functions
Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 129-134.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, it is proved that a topological space $X$ is a $QN$-space if and only if every image of the space $X$ under a Baire mapping to the Baire space $\mathbb{N}^{\mathbb{N}}$ is bounded. It is shown that there exists a compact $QN$-space such that its image under a Borel mapping to the Baire space $\mathbb{N}^{\mathbb{N}}$ is unbounded. The existence of such a space answers a question of L. Bukovský and J. Haleš. Generalizations of results of N. N. Kholshchevnikova concerning the representation of functions on subsets of the number line by trigonometric series are obtained.
Keywords: $QN$-space, $C_p$-theory, $\alpha_1$-property, Baire function
Mots-clés : quasinormal convergence, Baire space. 
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A. V. Osipov. On the Quasinormal Convergence of Functions. Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 129-134. http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a11/

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