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Mathematical Notes

, Volume 91, Issue 5–6, pp 789–799 | Cite as

Effective compactness and sigma-compactness

  • V. G. Kanovei
  • V. A. Lyubetsky
Article

Abstract

Using the Gandy-Harrington topology and other methods of effective descriptive set theory, we prove several theorems about compact and σ-compact sets. In particular, it is proved that any Δ 1 1 -set A in the Baire space N either is an at most countable union of compact Δ 1 1 -sets (and hence is σ-compact) or contains a relatively closed subset homeomorphic to N (in this case, of course, A cannot be σ-compact).

Keywords

effective descriptive set theory effectively compact σ-compact the Baire space Gandy-Harrington topology Δ11-set 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Institute for Problems of Information TransmissionMoscowRussia

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