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The diagonal limits of Hamming spaces. (English) Zbl 1321.54041

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)].

MSC:

54B35 Spectra in general topology
54E35 Metric spaces, metrizability
54E40 Special maps on metric spaces

Citations:

Zbl 1153.54004
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