Abstract
In this paper we investigate aspects of effectivity and computability on closed and compact subsets of locally compact spaces. We use the framework of the representation approach, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. This work is a generalization of the concepts introduced in [4] and [22] for the Euclidean case and in [3] for metric spaces. Whenever reasonable, we transfer a representation of the set of closed or compact subsets to locally compact spaces and discuss its properties and their relations to each other.
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