Definition
A space having at least one compactification whose remainder is zero-dimensional in the sense of inductive dimension is called an almost π-compact space.
Reference
L. G. Zambakhidze, On ther interrelations among the peripheral properties of Tikhonov spaces, their powers, exponentials, free groups, and semigroups, Russ. Math. Surv. 34:256 (1979) 256-260.