• Corpus ID: 226226742

Borel and analytic sets in locales.

@article{Chen2020BorelAA,
  title={Borel and analytic sets in locales.},
  author={Ruiyuan Chen},
  journal={arXiv: Logic},
  year={2020}
}
  • Ruiyuan Chen
  • Published 1 November 2020
  • Mathematics
  • arXiv: Logic
We systematically develop analogs of basic concepts from classical descriptive set theory in the context of pointless topology. Our starting point is to take the elements of the free complete Boolean algebra generated by the frame $\mathcal{O}(X)$ of opens to be the "$\infty$-Borel sets" in a locale $X$. We show that several known results in locale theory may be interpreted in this framework as direct analogs of classical descriptive set-theoretic facts, including e.g., the Lusin separation… 
On the Pettis-Johnstone theorem for localic groups
We explain how Johnstone’s 1989 proof of the closed subgroup theorem for localic groups can be viewed as a point-free version of Pettis’s theorem for Baire topological groups. We then use it to

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