The diagonal limits of Hamming spaces

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].