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Separation axioms and partitions of the set of natural numbers. (English. Russian original) Zbl 0813.03029

Sib. Math. J. 34, No. 3, 468-471 (1993); translation from Sib. Mat. Zh. 34, No. 3, 81-85 (1993).
The following question is investigated. Given an equivalence relation \(\mu\) on the set of natural numbers, under what conditions are its equivalence classes separated by recursive (or recursively enumerable) sets which are closed under \(\mu\)? It is shown that the answer is closely related to the properties of the topological space generated by the recursive (or recursively enumerable) sets that are closed under \(\mu\).

MSC:

03D45 Theory of numerations, effectively presented structures
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References:

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