Closedness Of Set Research Articles

Regularity of Center Manifolds via the Graph Transform

The purpose of this paper is to give a short self-contained proof of the center-manifold theorem for maps and vector fields in finite-dimensional spaces using the graph transform. In particular, regularity of the center manifold is established using a direct argument that is based on the closedness of sets of differentiable functions whose highest derivatives are Lipschitz continuous in the space of continuous functions; this argument avoids the fiber contraction theorem that is commonly used in this context.

Замкнутость множества сумм рядов Дирихле

Замкнутость множества сумм рядов Дирихле

Convexity and closedness of sets with respect to cones

Convexity and closedness of sets with respect to cones