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Connecting locally compact abelian groups


Authors: Ed Enochs and Walt Gerlach
Journal: Proc. Amer. Math. Soc. 89 (1983), 351-354
MSC: Primary 22B05
DOI: https://doi.org/10.1090/S0002-9939-1983-0712650-3
MathSciNet review: 712650
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Abstract: Those locally compact abelian groups having connected envelopes are characterized as those $ G$ such that the dimension of $ {\operatorname{Hom }}(G,R)$ over $ R$ is finite (where $ R$ is the field of real numbers).


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

  • [1] J. Sonner, Universal and special problems, Math. Z. 82 (1963), 200-211. MR 0156880 (28:123)
  • [2] E. Enochs, Injective and flat covers, envelopes and resolvants, Israel J. Math 39 (1981), 189-209. MR 636889 (83a:16031)
  • [3] -, Torsion free covering modules, Proc. Amer. Math. Soc. 14 (1963), 884-889. MR 0168617 (29:5877)
  • [4] W. Gerlach, Connecting locally compact abelian groups, Ph. D. thesis, Univ. of Kentucky, 1980.

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DOI: https://doi.org/10.1090/S0002-9939-1983-0712650-3
Article copyright: © Copyright 1983 American Mathematical Society

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