Porosity and the bounded linear regularity property
H. H. Bauschke and J. M. Borwein showed that in the space of all tuples of bounded,
closed and convex subsets of a Hilbert space with a nonempty intersection, a typical
tuple has the bounded linear regularity property. This property is important because
it leads to the convergence of infinite products of the corresponding nearest point
projections to a point in the intersection.
We show that the subset of all tuples possessing the bounded linear
regularity property has a porous complement. Moreover, our result is
established in all normed spaces and for tuples of closed and convex sets
which are not necessarily bounded. This is joint work with A. J. Zaslavski.