A null pseudohomotopic map onto a pseudo arc

posed by W. Kuperberg, asks whether the pseudo-arc is pseudo-contractible. This question remains open, but it will be shown here that there is a null pseudohomotopic map from a Cantor set onto a pseudo arc. The existence of such a map is quite some distance from settling the ques tion of pseudocontractibility, but by sidestepping some of the difficulties involving connectedness, it shows that some natural simple approaches are not powerful enough to prove non-pseudocontractibility. A continuum is a compact, connected metric space. A continuum is indecomposable if it is not the union of two of its proper subcontinua, and is hereditarily inde composable if each of its subcontinua is indecomposable. If a and b are points of an indecomposable continuum X, then a and b are in the same composant of X provided some proper subcontinuum of X contains both a and b. This is easily seen to be an equivalence relation, and each equivalence class (composant) is a first category Fa set. Thus, the complement of any composant is a dense Go