Abstract.Observations concerning the product of R. Pol's weakly infinitedimensional uncountable-dimensional compactum with various spaces are made. A proof showing that the product of a C-space and a compact Cspace is again a C-space is given. Related questions, motivated by this result, are asked.

Abstract.Observations concerning the product of R. Pol's weakly infinitedimensional uncountable-dimensional compactum with various spaces are made. A proof showing that the product of a C-space and a compact Cspace is again a C-space is given. Related questions, motivated by this result, are asked.

Abstract. We show that refinable maps defined on compacta preserve Property C. H. Kato has proved the analogous result for weakly infinite dimensional spaces. We also show that if / is a map from a compact C space X onto a non C space Y, then the set of points in Y with an uncountable number of preimages is a space that does not have Property C.

ABSTRACT. A map into the Hubert cube is stable if each composition with projection onto a finite number of factors is stable.We prove that a map from a compact metric space into the Hubert cube is stable if and only if it is universal. As a consequence, the composition of a stable map with any self homeomorphism of the Hilbert cube is also stable.

Abstract.It is shown that the product of a weakly infinite-dimensional compactum with a C-space is weakly infinite-dimensional.Some observations on the coincidence of weak infinite-dimensionality and property C are made. The question of when a weakly infinite-dimensional space has weakly infinitedimensional product with all zero-dimensional spaces is investigated.