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

Effective local compactness and the hyperspace of located sets