A new graph topology. connections with the compact open topology

Abstract

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 Ε 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.

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Notes on contributors

Primo Brandi