# Effective local compactness and the hyperspace of located sets

arXiv: https://arxiv.org/abs/1903.05490 · HTML: https://mlsanity.com/paper/1903.05490/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [A Computability Perspective on (Verified) Machine Learning](https://mlsanity.com/paper/2102.06585/) (2021)

## Abstract (arXiv)

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.