Can an group be anti-self-dual?
Abstract: We say that a topological group is anti-self-dual if there are no nontrivial continuous homomorphisms from into the character group or from into . We show that no nontrivial LCA group can be anti-self-dual.
-  Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
-  Lewis C. Robertson, Connectivity, divisibility, and torsion, Trans. Amer. Math. Soc. 128 (1967), 482–505. MR 0217211, https://doi.org/10.1090/S0002-9947-1967-0217211-6
-  -, Transfinite torsion, -constituents, and splitting in locally compact abelian groups, Mimeographed Notes, University of Washington, Seattle, Wash.
- E. Hewitt and K. Ross, Abstract harmonic analysis. Vol. 1: Structure of topological groups. Integration theory, group representations, Die Grundlehren der math. Wissenschaften, Band 115, Academic Press, New York and Springer-Verlag, Berlin, 1963. MR 28 #158. MR 551496 (81k:43001)
- L. C. Robertson, Connectivity, divisibility, and torsion, Trans. Amer. Math. Soc. 128 (1967), 482-505. MR 36 #302. MR 0217211 (36:302)
- -, Transfinite torsion, -constituents, and splitting in locally compact abelian groups, Mimeographed Notes, University of Washington, Seattle, Wash.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22.20
Retrieve articles in all journals with MSC: 22.20
Keywords: Continuous homomorphisms, character group, densely divisible, reduced, anti-self-dual, compact elements
Article copyright: © Copyright 1971 American Mathematical Society