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Topologically free subsets of universal algebras

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Ukrainian Mathematical Journal Aims and scope

Abstract

We prove that every infinite Abelian algebra and every countable field contain infinite topologically free subsets.

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References

  1. A. A. Markov, “On free topological groups,” Dokl. Akad. Nauk SSSR, 31, No. 4, 299–301 (1941).

    Google Scholar 

  2. A. A. Markov, “On free topological groups,” Izv. Akad. Nauk SSSR, Ser. Mat., No. 9, 3–64 (1945).

    Google Scholar 

  3. A. I. Mal’tsev, “Free topological groups,” Izv. Akad. Nauk SSSR, Ser. Mat., No. 2, 171–198 (1957).

    Google Scholar 

  4. M. M. Choban and S. S. Dumitrashku, “On universal algebras with continuous signature,” Usp. Mat. Nauk, 36, No. 5, 201–202 (1981).

    MATH  MathSciNet  Google Scholar 

  5. E. G. Zelenyuk and I. V. Protasov, “Topologies on Abelian groups,” Izv. Akad. Nauk. SSSR, Ser. Mat., No. 5, 1090–1107 (1990).

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  6. D. B. Shakhmatov, “Imbeddings in topological fields and the construction of a field whose space is not normal,” Comment. Math. Univ. Carolina, 24, No. 3, 525–540 (1983).

    MATH  MathSciNet  Google Scholar 

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Authors
  1. E. G. Zelenyuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 651–661, May, 1997.

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Zelenyuk, E.G. Topologically free subsets of universal algebras. Ukr Math J 49, 724–734 (1997). https://doi.org/10.1007/BF02486453

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  • DOI: https://doi.org/10.1007/BF02486453

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