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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Mukhin, Yu. N. 1985. Topological groups. Journal of Soviet Mathematics, Vol. 28, Issue. 6, p. 825.
    Lalithambal, R. 1972. On theorems of Thornton. Bulletin of the Australian Mathematical Society, Vol. 6, Issue. 02, p. 211.
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Torsion topological groups with minimal open sets

  • M.C. Thornton (a1)
Abstract

Torsion topological groups with the additional property that the intersection of open sets is open are considered and their topological structure is determined:

1) the topology is uniquely determined by a normal subgroup;

2) each group is uniquely an extension of an indiscrete group by a discrete group;

3) the topology may be changed within limits without changing the dual group.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1971
References
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[1]Alexandroff, P., “Diskrete Räume”, Rec. Math. Moscou (N.S.) 2 (1937), 501–518.
[Z]Hewitt, Edwin and Ross, Kenneth A., Abstract harmonic analysis, Vol. I (Die Grundlehren der mathematischen Wissenschaften, Band 115; Academic Press, New York; Springer-Verlag, Berlin, Göttingen, Heidelberg, 1963).
[3]Husain, Taqdir, Introduction to topologicul groups (W.B. Saunders, Philadelphia, London, 1966).
[4]Krishnamurthy, V., “On the number of topologies on a finite set”, Amer. Math. Monthly 73 (1966), 154–157.
[5]McCord, Michael C., “Singular homology groups and homotopy groups of finite topological spaces”, Duke Math. J. 33 (1966), 465–474.
[6]Morris, Sidney A. and Thompson, H.B., “Topologies on finite groups”, Bull. Austral. Math. Soc. 1 (1969), 315–317.
[7]Stephen, D., “Topology on finite sets”, Amer. Math. Monthly 75 (1968), 739–741.
[8]Stong, R.E., “Finite topological spaces”, Trans. Amer. Math. Soc. 123 (1966), 325–340.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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