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Topological results of sequences \(\{n_k x\}^\infty_{k=1}\) and their applications in the theory of trigonometric series. (English) Zbl 0924.40006
All results of this paper are based on Theorem 1.1 which describes from the topological point of view the behaviour of fractional parts of numbers \(n_kx\) \((k=1,2,\dots)\), where \(x\in\mathbb{R}\) and \(\{n_k\}^\infty_{k=1}\) is a given sequence of positive integers. In the second part of the paper we give a new proof of the categorical analogue of the well-known theorem of Cantor and Lebesgue.
MSC:
40J05 Summability in abstract structures
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
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References:
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