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Weakening Topologies on a Countable Abelian group of Finite Exponent

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Abstract

We prove that a countable locally minimal Abelian group of finite exponent m is discrete. For prime m, this answers Question 7.35(b) from [2].

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References

  1. L. Ausenhofer, M. J. Chasco, D. Dikranjan, and X. Domingues, “Locally minimal topological groups 1,” J. Math. Anal. Appl., 370, 431-452 (2010).

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  2. D. Dikranjan and M. Megrelishvili, “Minimality conditions in topological groups,” in: Recent Progress in General Topology III, edited by K. P. Hart, Jan van Mill, and P. Simon, Springer (Atlantis Press), Berlin, 2014, pp. 229-237.

  3. I. Protasov, Weakening topologies on a countable Boolean group, preprint.

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Correspondence to Igor Protasov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 1, pp. 58–59 January–March, 2020.

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Protasov, I. Weakening Topologies on a Countable Abelian group of Finite Exponent. J Math Sci 248, 188–189 (2020). https://doi.org/10.1007/s10958-020-04868-0

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  • DOI: https://doi.org/10.1007/s10958-020-04868-0

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