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Topologies On Groups Determined By Sequences: Answers To Several Questions Of I.protasov And E.zelenyuk
TOPOLOGIES ON GROUPS DETERMINED
TOPOLOGIES ON GROUPS DETERMINED
Abstract. Answering questions of Protasov and Zelenyuk we prove the following results: 1. For every increasing function f : N → N with limn→∞ f(n + 1) − f(n) = ∞ and every metrizable totally bounded group topology τ on Z there exists a convergent to zero sequence (an)n∈ω in (Z, τ ) such that limn→∞ an f(n) = 1. 2. For every real r > 1 there exists a sequence (an)n∈ω ⊂ Z such that limn→∞ an+1 an = r but there is no ring topology τ on Z such that (an)n∈...
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