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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2011 Volume 90, Issue 3, Pages 408–421 (Mi mzm6616)

This article is cited in 1 paper

Embedding of Products $Q(k)\times B(\tau)$ in Absolute $A$-Sets

S. V. Medvedev

South Ural State University, Chelyabinsk

Abstract: Theorems about closed embeddings in absolute $A$-sets of the products $Q(k)\times B(\tau)$, $Q(k)\times \nobreak\mathscr N$, and $Q(k)\times C$ are proved. These are generalizations to the nonseparable case of theorems of Saint-Raymond, van Mill, and van Engelen about closed embeddings in separable absolute Borel sets of the products $Q\times \mathscr N$ and $Q\times C$, where $Q$ is the space of rational numbers, $C$ is the Cantor perfect set, and $\mathscr N$ is the space of irrational numbers.

Keywords: rational and irrational numbers, Cantor set, absolute $A$-set, $G_\delta$-set, $F_\sigma$-set, closed embedding, metric space, complete metric space, absolute Borel set, Baire space.

UDC: 515.128

Received: 27.10.2008

DOI: 10.4213/mzm6616


 English version:
Mathematical Notes, 2011, 90:3, 398–410

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