This article is cited in 2 papers

RESEARCH ARTICLE

The diagonal limits of Hamming spaces

B. Oliynyk

Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, Volodymyrska 64, Kyiv, 01601, Ukraine

Abstract: 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, Besicovitch space, supernatural number, rooted tree, Bernoulli measure.

MSC: 54B35, 54E35, 54E40

Received: 11.04.2013
Revised: 18.04.2013

Language: English

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