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On finite approximations of topological algebraic systems. (English) Zbl 1115.03096
In this paper the concept of approximation of a topological algebraic system by finite algebraic systems from a given class is introduced and discussed. The following results are proved:
1. No infinite locally compact field can be approximated by finite associative rings;
2. For every uniformly locally compact algebra \(A\), there exists a hyperfinite approximation of \(A\);
3. No infinite locally compact field is abstractly approximable by finite associative rings.
MSC:
03H05 Nonstandard models in mathematics
54H13 Topological fields, rings, etc. (topological aspects)
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