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Proceedings of the American Mathematical Society

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The normal extensions of subgroup topologies

Authors: Bradd Clark and Victor Schneider
Journal: Proc. Amer. Math. Soc. 97 (1986), 163-166
MSC: Primary 22A05
MathSciNet review: 831407
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Abstract: Let $ H$ be a topological group contained in a group $ G$. A topology which makes $ G$ a topological group inducing the given topology on $ H$ is called an extending topology. The set of all extending topologies forms a complete semilattice in the lattice of group topologies on $ G$. The structure of this semilattice is studied by considering normal subgroups which intersect $ H$ in the identity.

References [Enhancements On Off] (What's this?)

  • [1] B. Clark and V. Schneider, The extending topologies, Internat. J. Math. Math. Sci. 7 (1984), 621-623. MR 771611 (86e:22002)
  • [2] -, All knot groups are metric, Math. Z. 187 (1984), 269-271. MR 753437 (85i:57003)
  • [3] E. Hewitt and K. Ross, Abstract harmonic analysis. I, Springer-Verlag, New York, 1963.

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Keywords: Lattice, group topologies
Article copyright: © Copyright 1986 American Mathematical Society

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