Forbidden rectangles in compacta

We establish negative results about “rectangular” local bases in compacta. For example, there is no compactum where all points have local bases of cofinal type ω×ω2. For another, the compactum βω has no nontrivially rectangular local bases, and the same is consistently true of βω∖ω: no local base in βω has cofinal type κ×c if κ