Hilbert space is homeomorphic to the countable infinite product of lines

Abstract

In this paper, Hilbert space, denoted by / 2 , is understood to be the space of all sequences (#*) such that X)i #?< with d((Xi), (^)) = (2ri (*-*) 2 ) 1/2 . We let the countable infinite product of lines be regarded as s==ILLi /? where, for each i>0, I? denotes the open interval (0, 1).