Geodesic
The diagonal limits of Hamming spaces
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 229-236 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 subspace coincides with the completion of the space of all periodic sequences on the alphabet $B$. Then we give answers on two questions formulated in [1].
Keywords: Hamming space, diagonal limit, supernatural number, rooted tree, Bernoulli measure.
Mots-clés : Besicovitch space 
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B. Oliynyk. The diagonal limits of Hamming spaces. Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 229-236. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a7/

[1] P. J. Cameron, S. Tarzi, “Limits of cubes”, Topology and its Applications, 155:14 (2008), 1454–1461 | DOI | MR | Zbl

[2] F. Blanchard, E. Formenti, P. Kurka, “Cellular automata in the Cantor, Besicovitch, and Weyl topological spaces”, Complex Systems, 11:2 (1997), 107–123 | MR | Zbl

[3] Funct. Anal. Appl., 45:3 (2011), 173–186 | DOI | DOI | MR | Zbl

[4] St. Petersburg Math. J., 6:4 (1995), 705–761 | MR | Zbl

[5] B. V. Oliynyk, V. I. Sushchanskii, “The isometry groups of the Hamming spaces of periodic sequences”, Siberian Mathematical Journal, 54:1 (2013), 124–136 | DOI | MR | Zbl

[6] R. I. Grigorchuk, V. V. Nekrashevich, V. I. Sushchanskii, “Automata, dynamical systems, and groups”, Proc. Steklov Inst. Math., 231, 2000, 128–203 (Russian) | MR | Zbl