Oliynyk, Bogdana The diagonal limits of Hamming spaces. (English) Zbl 1321.54041 Algebra Discrete Math. 15, No. 2, 229-236 (2013). Summary: We consider a continuum family of subspaces of the Besicovitch-Hamming space on some alphabet \(B\), naturally parametrized by supernatural numbers. Every subspace is defined as a diagonal limit of finite Hamming spaces on the alphabet \(B\). We present a convenient representation of these subspaces. Using this representation we show that the completion of each of these subspaces coincides with the completion of the space of all periodic sequences on the alphabet \(B\). Then we give answers on two questions formulated in [P. J. Cameron and S. Tarzi, Topology Appl. 155, no. 14, 1454–1461 (2008; Zbl 1153.54004)]. Cited in 2 Documents MSC: 54B35 Spectra in general topology 54E35 Metric spaces, metrizability 54E40 Special maps on metric spaces Keywords:Hamming space; diagonal limit; Besicovitch space; supernatural number; rooted tree; Bernoulli measure Citations:Zbl 1153.54004 PDFBibTeX XMLCite \textit{B. Oliynyk}, Algebra Discrete Math. 15, No. 2, 229--236 (2013; Zbl 1321.54041)