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. 
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/
@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},
     year = {2022},
     volume = {19},
     number = {1},
     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
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
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a9/
%G en
%F SEMR_2022_19_1_a9

[1] R. Kornev, “A semilattice of degrees of computable metrics”, Sib. Math. J., 62:5 (2021), 822–841 | DOI | MR | Zbl

[2] Ch. Kreitz, K. Weihrauch, “Theory of representations”, Theoret. Comput. Sci., 38 (1985), 35–53 | DOI | MR | Zbl

[3] K. Weihrauch, Computable analysis. An introduction, Texts in Theoret. Comput. Sci. EATCS Ser., Springer, Berlin, 2000 | DOI | MR | Zbl

[4] R. Kornev, “Computable metrics above the standard real metric”, Sib. Èlectron. Mat. Izv., 18:1 (2021), 377–392 | DOI | MR | Zbl

[5] R. Dillhage, Computable functional analysis. Compact operators on computable Banach spaces and computable best approximation, PhD Thesis, Fak. Math. Inform., FernUniversität Hagen, 2012