Geodesic
Topological Spaces over Algorithmic Representations of Universal Algebras
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 17-29.

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

In this paper, we examine topological spaces that can be effectively defined over factor sets modulo equivalences on the set of natural numbers. We formulate a criterion of computable (effective) separability of topological spaces in terms of the approximability of the corresponding algebras by negative (uniformly effectively separated) algebras. We compare negative and positive algebra representations from the standpoint of the structure of the corresponding effective spaces. For effective infinite topological spaces, we prove the existence of their infinite effective compact extensions.
Keywords: numbering, positivity, negativity, algorithmic representation of algebra, computable space, effective space. 
@article{INTO_2018_144_a1,
     author = {N. Kh. Kasymov and I. A. Khodzhamuratova},
     title = {Topological {Spaces} over {Algorithmic} {Representations} of {Universal} {Algebras}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {17--29},
     publisher = {mathdoc},
     volume = {144},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_144_a1/}
}
TY  - JOUR
AU  - N. Kh. Kasymov
AU  - I. A. Khodzhamuratova
TI  - Topological Spaces over Algorithmic Representations of Universal Algebras
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 17
EP  - 29
VL  - 144
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_144_a1/
LA  - ru
ID  - INTO_2018_144_a1
ER  - 
%0 Journal Article
%A N. Kh. Kasymov
%A I. A. Khodzhamuratova
%T Topological Spaces over Algorithmic Representations of Universal Algebras
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 17-29
%V 144
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_144_a1/
%G ru
%F INTO_2018_144_a1
N. Kh. Kasymov; I. A. Khodzhamuratova. Topological Spaces over Algorithmic Representations of Universal Algebras. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 17-29. http://geodesic.mathdoc.fr/item/INTO_2018_144_a1/

[1] Goncharov S. S., Ershov Yu. L., Konstruktivnye modeli, Nauchnaya kniga, Novosibirsk, 1999 | MR

[2] Ershov Yu. L., Teoriya numeratsii, Nauka, M., 1977 | MR

[3] Ershov Yu. L., Problemy razreshimosti i konstruktivnye modeli, Nauka, M., 1980

[4] Kasymov N. Kh., “Ob algebrakh s finitno approksimiruemymi pozitivno predstavimymi obogascheniyami”, Algebra i logika, 26:6 (1987), 715–730 | MR

[5] Kasymov N. Kh., “Pozitivnye algebry s kongruentsiyami konechnogo indeksa”, Algebra i logika, 30:3 (1991), 293–305 | MR

[6] Kasymov N. Kh., “Pozitivnye algebry so schetnymi reshetkami kongruentsii”, Algebra i logika, 31:1 (1992), 21–37 | MR | Zbl

[7] Kasymov N. Kh., “O gomomorfizmakh na negativnye algebry”, Algebra i logika, 31:2 (1992), 132–144 | MR | Zbl

[8] Kasymov N. Kh., “O chisle kongruentsii algebr nad prostymi mnozhestvami”, Mat. zametki, 51:3 (1992), 150–152

[9] Kasymov N. Kh., “Aksiomy otdelimosti i razbieniya naturalnogo ryada”, Sib. mat. zh., 34:3 (1993), 81–85 | MR | Zbl

[10] Kasymov N. Kh., “Numerovannye algebry s ravnomerno rekursivno otdelimymi klassami”, Sib. mat. zh., 34:5 (1993), 85–102 | MR | Zbl

[11] Kasymov N. Kh., “Ob algebrakh nad negativnymi ekvivalentnostyami”, Algebra i logika, 33:1 (1994), 76–80 | MR | Zbl

[12] Kasymov N. Kh., “Rekursivno otdelimye numerovannye algebry”, Usp. mat. nauk, 51:3 (1996), 145–176 | DOI | MR | Zbl

[13] Kasymov N. Kh., “O gomomorfizmakh na effektivno otdelimye algebry”, Sib. mat. zh., 57:1 (2016), 47–66 | MR | Zbl

[14] Maltsev A. I., “Konstruktivnye algebry (I)”, Usp. mat. nauk, 16:3 (1961), 3–60 | MR | Zbl

[15] Maltsev A. I., Algoritmy i rekursivnye funktsii, Nauka, M., 1986 | MR

[16] Uspenskii V. A., “O vychislimykh operatsiyakh”, Dokl. AN SSSR, 103:5, 773–776 | MR

[17] Uspenskii V. A., “Sistemy perechislimykh mnozhestv i ikh numeratsii”, Dokl. AN SSSR, 105:6 (1955), 1155–1158