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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.
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
Linking options:
https://www.mathnet.ru/eng/mzm6616https://doi.org/10.4213/mzm6616 https://www.mathnet.ru/eng/mzm/v90/i3/p408
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Abstract page: | 504 | Full-text PDF : | 185 | References: | 69 | First page: | 5 |
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