Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661187 | Topology and its Applications | 2006 | 11 Pages |
Abstract
A sequence {an} in a group G is a T-sequence if there is a Hausdorff group topology τ on G such that . In this paper, we provide several sufficient conditions for a sequence in an abelian group to be a T-sequence, and investigate special sequences in the Prüfer groups Z(p∞). We show that for p≠2, there is a Hausdorff group topology τ on Z(p∞) that is determined by a T-sequence, which is close to being maximally almost-periodic—in other words, the von Neumann radical n(Z(p∞),τ) is a non-trivial finite subgroup. In particular, n(n(Z(p∞),τ))⊊n(Z(p∞),τ). We also prove that the direct sum of any infinite family of finite abelian groups admits a group topology determined by a T-sequence with non-trivial finite von Neumann radical.
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Physical Sciences and Engineering
Mathematics
Geometry and Topology