Let X be a metric space, and C the collection of all nonempty closed subsets of X. Let G = {graph(f,Ω): Ω ∈ C and f:X → Rm is continuous}, where graph(f,Ω) = {(x, f (x)) ∈ X × Rm : x ∈ Ω}. The notion of cK-convergence (Kuratowski convergence on compact sets) in G is defined and characterized, and its relationships with other types of convergence in G are explored. These results allow a comparison between the topology induced by cK-convergence and various other graph space topologies.

Kuratowski convergence on compact sets

Sampalmieri Rosella
1992-01-01

Abstract

Let X be a metric space, and C the collection of all nonempty closed subsets of X. Let G = {graph(f,Ω): Ω ∈ C and f:X → Rm is continuous}, where graph(f,Ω) = {(x, f (x)) ∈ X × Rm : x ∈ Ω}. The notion of cK-convergence (Kuratowski convergence on compact sets) in G is defined and characterized, and its relationships with other types of convergence in G are explored. These results allow a comparison between the topology induced by cK-convergence and various other graph space topologies.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/120942
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