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Anagrafe della Ricerca dell'Università degli Studi di Perugia.
EnglishLet (X,d) be a boundedly compact metric space and C be the set of all closed nonempty subsets of X. For a closed subset E, let G_E denote the set of all graphs of continuous functions in C(E,R^m); and let G = UG_E. A new topology, called the \tau-topology, is defined on G, and it is shown that the topological space (G,\tau) is homeomorphic to the quotient space [(C,\tau)x(X,R^m)]/W with a suitable equivalence relation W. The topological subspace (G_E,\tau) is homeomorphic to the space C(E,R^m) for every fixed closed subset E . The obtained results are useful for proving existence and continuous dependence results for solutions of ordinary and partial differential equations with hereditary structure.
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| Titolo: | A new graph topology intended for functional differential equations |
| Autori: | |
| Data di pubblicazione: | 1996 |
| Rivista: | |
| Abstract: | Let (X,d) be a boundedly compact metric space and C be the set of all closed nonempty subsets of ...X. For a closed subset E, let G_E denote the set of all graphs of continuous functions in C(E,R^m); and let G = UG_E. A new topology, called the \tau-topology, is defined on G, and it is shown that the topological space (G,\tau) is homeomorphic to the quotient space [(C,\tau)x(X,R^m)]/W with a suitable equivalence relation W. The topological subspace (G_E,\tau) is homeomorphic to the space C(E,R^m) for every fixed closed subset E . The obtained results are useful for proving existence and continuous dependence results for solutions of ordinary and partial differential equations with hereditary structure. |
| Handle: | http://hdl.handle.net/11391/918911 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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