Effective local compactness and the hyperspace of located sets

03/13/2019

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by   Arno Pauly, et al.

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We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness suffices to ensure that the hyperspace of closed-and-overt sets (aka located sets, aka closed sets with full information) is computably compact and computably metrizable.