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. 
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     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},
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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/