The convergence of the projection algorithm for solving the convex
feasibility problem for a family of closed convex sets, is in connection with
the regularity properties of the family. In the paper [18] are pointed out four
cases of such a family depending of the two characteristics: the emptiness and
boudedness of the intersection of the family. The case four (the interior of
the intersection is empty and the intersection itself is bounded) is unsolved.
In this paper we give a (partial) answer for the case four: in the case of two
closed convex sets in R3 the regularity property holds.Comment: 14 pages, exposed on 5th International Conference "Actualities and
Perspectives on Hardware and Software" - APHS2009, Timisoara, Romani