Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-13T19:47:07.388Z Has data issue: false hasContentIssue false
  • English
  • Français

On Pontryagin duality

Published online by Cambridge University Press:  18 May 2009

B. J. Day
B. J. Day
Affiliation:
Department of Pure Mathematics, University of Sydney, N.S.W. 2006, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The main aim of this article is to discuss the relationship between Pontryagin duality and pro-objects. The basic idea arises from K. H. Hofmann's articles [7] and [8] where it is shown that the elementary abelian (Lie) groups are “dense” in the category of locally compact hausdorff abelian groups.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 1 , January 1979, pp. 15 - 24
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Day, Brian, On adjoint-functor factorisation, in Category Seminar Sydney 1972/73, Lecture Notes in Mathematics 420 (Springer-Verlag, 1974), 1–19.CrossRefGoogle Scholar
2.Day, B. J., Density presentations of functors, Bull. Austral. Math. Soc. 16 (1977), 427–448.CrossRefGoogle Scholar
3.Day, B. J. and Kelly, G. M., Enriched functor categories, in Reports of the Midwest Category Seminar III, Lecture Notes in Mathematics 106 (Springer-Verlag, 1969), 178–191.CrossRefGoogle Scholar
4.Dubuc, Eduardo J., Kan extensions in enriched category theory, Lecture Notes in Mathematics 145 (Springer-Verlag, 1970).CrossRefGoogle Scholar
5.Eilenberg, Samuel and Kelly, G. Max, Closed categories, in Proceedings of the Conference on Categorical Algebra, La Jolla, California, 1965(Springer-Verlag, 1966), 421–562.CrossRefGoogle Scholar
6.Hochschild, G., The structure of Lie groups, (Holden-Day Inc., 1965).Google Scholar
7.Hofmann, Karl Heinrich, Categories with convergence, exponential functors, and cohomology of compact abelian groups, Math. Z. 104 (1968), 106–140.CrossRefGoogle Scholar
8.Hofmann, Karl Heinrich, Category theoretical methods in topological algebra, in Categorical topology Mannheim 1975 (Springer-Verlag, 1976), 345–403.Google Scholar
9.Hofmann, Karl Heinrich, Mislove, Michael and Stralka, Albert, The Pontryagin duality of compact O-dimensional semilattices and its applications, Lecture Notes in Mathematics 396 (Springer-Verlag, 1974).CrossRefGoogle Scholar
10.Kaplan, Samuel, Extensions of the Pontryagin duality I: infinite products, Duke Math. J. 15 (1948), 649–658.CrossRefGoogle Scholar
11.Kaplan, Samuel, Extensions of the Pontryagin duality II: direct and inverse sequences, Duke Math. J. 17 (1950), 419–435.CrossRefGoogle Scholar
12.Lane, S. Mac, Categories for the working mathematician, Graduate Texts in Mathematics 5 (Springer-Verlag, 1971).CrossRefGoogle Scholar
13.Numakura, K., Theorems on compact totally disconnected semigroups and lattices, Proc. Amer. Math. Soc. 8 (1957), 623–626.CrossRefGoogle Scholar