Let C be the set of all the closed nonempty subsets of R. Given a closed subset E let G_E denote the set of all the graphs of continuous functions in C(E,R^m). Let G =U G_E. We endow G with a new topology, called \tau-topology. It is strictly coarser than the Hausdorff metric topology and strictly finer than the topology of uniform convergence of distance functionals on bounded sets of R^(m+1). The topological space(G,\tau) is homeomorphic to the quotient space [(C,\tau)xC(R,R^m)]/W with a suitable equivalence relation W. The relationships between the \tau-topology and the topologies introduced on G_E by other authors are explored.
A new graph topology. Connections with the compact open topology
BRANDI, Primo;CEPPITELLI, Rita
1994
Abstract
Let C be the set of all the closed nonempty subsets of R. Given a closed subset E let G_E denote the set of all the graphs of continuous functions in C(E,R^m). Let G =U G_E. We endow G with a new topology, called \tau-topology. It is strictly coarser than the Hausdorff metric topology and strictly finer than the topology of uniform convergence of distance functionals on bounded sets of R^(m+1). The topological space(G,\tau) is homeomorphic to the quotient space [(C,\tau)xC(R,R^m)]/W with a suitable equivalence relation W. The relationships between the \tau-topology and the topologies introduced on G_E by other authors are explored.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
