The diagonal limits of Hamming spaces

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].