On the basis of a given differentiable strictly convex function F(x) in Euclidean space En (n≥2) special manifolds in the topological sense, which have some interesting globally geometrical features, can be defined. These manifolds can be interpreted as well as optimal solution sets (sets of all optimal points) of certain nonlinear parametric optimization problems. The former article dealt with the function F(x) under stronger suppositions-F(x) was continuously differentiable at least of order two in En and the Hesse matrix of it was positive definite in the points x, where the gradient ∇F(x) was a nonzero vector. Some theorems of the present article differ from analogous ones of the former article so that they have weaker assumptions and the manifolds are here the manifolds in the topological sense-not generally smooth. The article contains then any further results.
