Topological Spaces Over Algorithmic Representations of Universal Algebras

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 nega...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-03, Vol.245 (3), p.311-322
Main Authors: Kasymov, N. Kh, Khodzhamuratova, I. A.
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
Number theory
Representations
Topology
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04692-6