Authors: Choban M. M., Afanas D. N.
Abstract
The question of when the spaces $C_p(X)$ and $C_p(Y)$ of continuous real-valued functions on $X$ and $Y$ in the topology of pointwise convergence are linearly homeomorphic is studied. This spaces are called $l_p$-equivalent. It is established that the absolutes of the dyadic infinite spaces $X$ and $Y$ of the weights $m$ and $n$ respectively are
$l_p$-equivalent if and only if $m^{\aleph _0}$=$n^{\aleph _0}$. An analogous result for the topology of uniform convergence was obtained by S.V.Kislyakov
Department of Mathematics, Tiraspol State University
str. Gh.Iablocichin 5, Chisinau, MD-2069 Moldova