A fiberable continuum which is not nontrivially productable II

Abstract

We construct a metric continuum X such that there exists a continuous surjection F from X onto X with the inverse image of every point of size of the continuum and such that for no nontrivial topological space T there exists a surjection from X onto X×T. In particular, F cannot be a composition of a surjection from X onto X×T and the projection onto X, where T is a topological space of size of the continuum with at least one nonempty open set not equal to the whole space. This is a sharpening of the result obtained in [2].