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Mat. Zametki, 2011, Volume 90, Issue 3, Pages 408–421 (Mi mz6616)  

This article is cited in 1 scientific paper (total 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

DOI: https://doi.org/10.4213/mzm6616

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

Bibliographic databases:

UDC: 515.128
Received: 27.10.2008

Citation: S. V. Medvedev, “Embedding of Products $Q(k)\times B(\tau)$ in Absolute $A$-Sets”, Mat. Zametki, 90:3 (2011), 408–421; Math. Notes, 90:3 (2011), 398–410

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Medvedev S.V., “On properties of $h$-homogeneous spaces with the Baire property”, Topology Appl., 159:3 (2012), 679–694  crossref  mathscinet  zmath  isi  elib  scopus
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