Rita Ceppitelli

Some further generalizations of Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities

On etablit des inegalites minimax generalisees pour des fonctions prenant des valeurs dans des espaces vectoriels ordonnes

Applications of the generalized Knaster-Kuratowski-Mazurkiewicz Theorem to variational inequalities

On presente des versions generalisees des resultats de M. Lassonde sur des inegalites de type variationnel en utilisant certaines extensions du theoreme de Knaster-Kuratowski-Mazurkiewicz

Existence, uniqueness, and continuous dependence for hereditary differential equations

Abstract In the setting of functional differential equations, an abstract hereditary structure is introduced which includes and unifies many formulations already considered by other authors. For the new structure, existence, uniqueness, and continuous dependence theorems are given.

A new graph topology. connections with the compact open topology

Let E be a closed connected subset of and let C be the set of all the closed non-empty subsets of E. Given Ω E С, let GΩ denote the set of all the graphs of continuous functions in . Let . We endow G with a new topology called Τ-topology. It is strictly coarser than Hausdorff metric topology and strictly finer than the topology of uniform convergence of distance functionals on bounded sets of The topological space (G,τ) is homeomorphic to the quotient space with a suitable equivalence relation R. The relationships between τ‐topology and the topologies introduced in GΩ by other Authors are explored.

A hypertopology intended for functional differential equations

Let (X,d) be a locally compact separable metric space, Y a Frechet space and let C be the of all the closed non-empty susbsets of X. Given ω ∈ C let G ω denote the set of all the graphs of continuous functions in C(ω Y). Let G=uω∈cGωWe endow G with a new topology called τ-topology. The topological space (G,τ) is homeomorphic to the quotient space [(C,r)×C(X,Y)]/R with respect to a suitable equivalence relation R. The relationships between τ-topology and the topologies in Cω by other Authors are explored. The results here obtained generlize those got in [12] and find applications in the theory of Ordinary and Partial Differential Equations with hereditary structure.

Preference orders and continuous representations

In this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.