Geodesic
Effective Compactness and Sigma-Compactness
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 840-852

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2012_91_6_a4,
     author = {V. G. Kanovei and V. A. Lyubetskii},
     title = {Effective {Compactness} and {Sigma-Compactness}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {840--852},
     publisher = {mathdoc},
     volume = {91},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a4/}
}
TY  - JOUR
AU  - V. G. Kanovei
AU  - V. A. Lyubetskii
TI  - Effective Compactness and Sigma-Compactness
JO  - Matematičeskie zametki
PY  - 2012
SP  - 840
EP  - 852
VL  - 91
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a4/
LA  - ru
ID  - MZM_2012_91_6_a4
ER  - 
%0 Journal Article
%A V. G. Kanovei
%A V. A. Lyubetskii
%T Effective Compactness and Sigma-Compactness
%J Matematičeskie zametki
%D 2012
%P 840-852
%V 91
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a4/
%G ru
%F MZM_2012_91_6_a4
V. G. Kanovei; V. A. Lyubetskii. Effective Compactness and Sigma-Compactness. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 840-852. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a4/