Attouch-Wets convergence and Kuratowski convergence on compact sets

@inproceedings{Piccione2010AttouchWetsCA,
  title={Attouch-Wets convergence and Kuratowski convergence on compact sets},
  author={Paolo Piccione and Rosella Sampalmieri},
  year={2010}
}
Let X be a locally connected, b-compact metric space and E a closed subset of X. Let G be the space of all continuous real-valued functions defined on some closed subsets of E. We prove the equivalence of the τ aw and τ K topologies on G, where τ aw is the so called Attouch-Wets topology, defined in terms of uniform convergence of distance functionals, and τ K is the topology of Kuratowski convergence on compacta. 

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