Amalgams, connectifications, and homogeneous compacta

We construct a path-connected homogeneous compactum with cellularity c 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 Ti spaces has a Ti pathwise connectification, where i∈{1,2,3,3.5}.