Characterizing stable complete ErdAs space

We focus on the space E (c) (omega) , the countable infinite power of complete ErdAs space E (c). Both spaces are universal spaces for the class of almost zerodimensional spaces. We prove that E (c) (omega) has the property that it is stable under multiplication with any complete almost zero-dimensional space. We obtain this result as a corollary to topological characterization theorems that we develop for E (c) (omega) . We also show that sigma-compacta are negligible in E (c) (omega) and that the space is countable dense homogeneous.