Geodesic
On the maximality of degrees of metrics under computable reducibility
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 248-258

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

We study the semilattice $\mathcal{CM}_c(\mathbf{X})$ of degrees of computable metrics on a Polish space $\mathbf{X}$ under computable reducibility. It is proved that this semilattice does not have maximal elements if $\mathbf{X}$ is a noncompact space. It is also shown that the degree of the standard metric on the unit interval is maximal in the respective semilattice.
Keywords: computable metric space, Cauchy representation, reducibility of representations, computable analysis. 
@article{SEMR_2022_19_1_a9,
     author = {R. Kornev},
     title = {On the maximality of degrees of metrics under computable reducibility},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {248--258},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a9/}
}
TY  - JOUR
AU  - R. Kornev
TI  - On the maximality of degrees of metrics under computable reducibility
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 248
EP  - 258
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a9/
LA  - en
ID  - SEMR_2022_19_1_a9
ER  - 
%0 Journal Article
%A R. Kornev
%T On the maximality of degrees of metrics under computable reducibility
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 248-258
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a9/
%G en
%F SEMR_2022_19_1_a9
R. Kornev. On the maximality of degrees of metrics under computable reducibility. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 248-258. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a9/