  Quite a few studies on real-world applications of multi-objective
optimization reported that their Pareto sets and Pareto fronts form a
topological simplex. Such a class of problems was recently named the simple
problems, and their Pareto set and Pareto front were observed to have a gluing
structure similar to the faces of a simplex. This paper gives a theoretical
justification for that observation by proving the gluing structure of the
Pareto sets/fronts of subproblems of a simple problem. The simplicity of
standard benchmark problems is studied.
