Let (X,d) be a locally compact separable metric space, Y a Frechet space and let C be the set of all the closed non-empty susbsets of X. Given a closed subset E, let G_E denote the set of all the graphs of continuous functions in C(E,Y). Let G=U G_E. We endow G with a new topology called \tau-topology. The topological space (G,\tau) is homeomorphic to the quotient space [(C,\tau)xC(X,Y)]/R with respect to a suitable equivalence relation R. The relationships between \tau-topology and the topologies introduced in G_E by other authors are explored. The results here obtained generalize those got by the authors in Appl. Analiysis, 53, (1994), 185-196 and find applications in the theory of Ordinary and Partial Differential Equations with hereditary structure.
A hypertopology intended for functional differential equations
BRANDI, Primo;CEPPITELLI, Rita
1997
Abstract
Let (X,d) be a locally compact separable metric space, Y a Frechet space and let C be the set of all the closed non-empty susbsets of X. Given a closed subset E, let G_E denote the set of all the graphs of continuous functions in C(E,Y). Let G=U G_E. We endow G with a new topology called \tau-topology. The topological space (G,\tau) is homeomorphic to the quotient space [(C,\tau)xC(X,Y)]/R with respect to a suitable equivalence relation R. The relationships between \tau-topology and the topologies introduced in G_E by other authors are explored. The results here obtained generalize those got by the authors in Appl. Analiysis, 53, (1994), 185-196 and find applications in the theory of Ordinary and Partial Differential Equations with hereditary structure.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
