RO  EN
IMI/Publicaţii/BASM/Ediţii/BASM n.3 (25), 1997/

On functional equivalence of extremally disconnected spaces. (English)

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