English

Effective local compactness and the hyperspace of located sets

Logic in Computer Science 2019-03-14 v1 Logic

Abstract

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.

Keywords

Cite

@article{arxiv.1903.05490,
  title  = {Effective local compactness and the hyperspace of located sets},
  author = {Arno Pauly},
  journal= {arXiv preprint arXiv:1903.05490},
  year   = {2019}
}

Comments

Working paper

R2 v1 2026-06-23T08:06:57.758Z