Non-productive duality properties of topological groups
by
Masasi Higasikawa
Eda Laboratory, School of Science and Engineering, Waseda University

We show that each of the following properties of Abelian topological groups is not preserved under direct products: ``Every closed subgroup is dually closed" and ``every closed subgroup is dually embedded." Thus we refute a remark in [1].

We utilize the group topologies determined by sequences ([2]) and invoke a theorem on exponential Diophantine equations.

References

1. N. Noble, k-groups and duality, Trans. Amer. Math. Soc. 151 (1970) 551-561.
2. E.G. Zelenyuk and I.V. Protasov, Topologies on abelian groups (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 1090-1107, translation in Math. USSR-Izv. 37 (1991) 445-460.

Date received: June 21, 2000