Porous Set

A subset E of a metric space (X,d) is porous if there exists a constant c ∈ (0,1) such that for every point x ∈ E and every sufficiently small radius r > 0 there exists a point y with the open ball B(y, c r) contained in B(x, r) bsp;\ E; intuitively E has holes of relative radius at least c at all small scales around each of its points.