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 Δ11-set A in the Baire space N either is an at most countable union of compact Δ11-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.
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