  We construct a path-connected homogenous compactum with cellularity 2^omega
that is not homeomorphic to any product of dyadic compacta and first countable
compacta. We also prove some closure properties for classes of spaces defined
by various connectifiability conditions. One application is that every infinite
product of infinite topological sums of T_i spaces has a T_i pathwise
connectification, where i is 1, 2, 3, or 3.5.
