Solution of a general version of Armacost's problem on topologically torsion elements

We consider an extended version of Armacost’s problem of “description of topologically torsion elements” of the circle group and describe topologically $$s$$ -torsion and topologically $$\alpha$$ -torsion elements (which form the statistically characterized subgroups and $$\alpha$$ -statistically characterized subgroups, recently developed in [16], [14] respectively) in terms of the support. Our main result Theorem 2.1 provides the answers to the open problems Problem 6.10 [16] and Problem 2.14 [14] (which was partially answered only for the sequence $$(2^n)$$ in [13]).