A note on the NFI-topology

Some notes on spaces of ideals and computable topology

We show some basic results on the characterization of quasi-Polish spaces in terms of spaces of ideals, with an emphasis on the connections with computable topology.

A note on an effective Polish topology and Silver's Dichotomy theorem

We define a Polish topology inspired from the Gandy-Harrington topology and show how it can be used to prove Silver's dichotomy theorem while remaining in the Polish realm. In this topology, a $Π^1_1$ equivalence relation decomposes into a "sum" of a clopen relation and a meager one. We characterize it as the largest regular toplogy with a basis included in $Σ^1_1$.

Topology of definable abelian groups in o-minimal structures

In this note we show that every definably connected, definably compact abelian definable group in an o-minimal expansion of a real closed field of dimension not 4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semialgebraic case the result holds for all dimensions.

关于可计算Étale空间的注记

A note on computable étale spaces

本文研究可计算Étale空间，将其与可计算函数联系起来，并探讨其在可计算范畴中的等价关系。