Using interval arithmetic to prove that a set is path-connected
In this paper, we give a numerical algorithm able to prove whether a set S described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as S. Examples illustrate the principle of the approach. (c) 2005 Elsevier B.V. All rights reserved.
interval arithmetic graph theory connected set topology set computation automatic proof