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This article is cited in 2 scientific papers (total in 2 papers)
Effective Compactness and Sigma-Compactness
V. G. Kanovei, V. A. Lyubetskii
A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
Abstract:
Using the Gandy–Harrington topology and other methods of effective descriptive set theory, we prove several theorems about compact and $\sigma$-compact sets. In particular, it is proved that any $\Delta_1^1$-set $A$ in the Baire space $\mathscr N$ either is an at most countable union of compact $\Delta_1^1$-sets (and hence is $\sigma$-compact) or contains a relatively closed subset homeomorphic to $\mathscr N$ (in this case, of course, $A$ cannot be $\sigma$-compact).
Keywords:
effective descriptive set theory, effectively compact, $\sigma$-compact, the Baire space, Gandy–Harrington topology, $\Delta^1_1$-set
DOI:
https://doi.org/10.4213/mzm8544
 Full text:
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English version:
Mathematical Notes, 2012, 91:6, 789–799
Bibliographic databases:
   
Document Type:
Article
UDC:
510.225
Received: 01.11.2009
Revised: 27.05.2011
Citation:
V. G. Kanovei, V. A. Lyubetskii, “Effective Compactness and Sigma-Compactness”, Mat. Zametki, 91:6 (2012), 840–852; Math. Notes, 91:6 (2012), 789–799
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/mz8544https://doi.org/10.4213/mzm8544 http://mi.mathnet.ru/eng/mz/v91/i6/p840
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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V. G. Kanovei, V. A. Lyubetskii, “On Effective $\sigma$-Boundedness and $\sigma$-Compactness in Solovay's Model”, Math. Notes, 98:2 (2015), 273–282
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Lyubetsky V.A. Seliverstov A.V., “A novel algorithm for solution of a combinatory set partitioning problem”, J. Commun. Technol. Electron., 61:6 (2016), 705–708
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