每个波兰群都具有非平凡的拓扑群自同构
逻辑
2025-12-12 v4
摘要
我们证明，每个拥有超过两个元素的波兰群都 admits 一个非平凡的拓扑群自同构。据此推论，若假设存在一个拥有超过两个点的唯一均匀波兰空间且该空间是半拓扑群，则必然矛盾。
引用
@article{arxiv.2408.16162,
title = {Every Polish group has a non-trivial topological group automorphism},
author = {Carlos Pérez Estrada and Ulises Ariet Ramos-García},
journal= {arXiv preprint arXiv:2408.16162},
year = {2025}
}
备注
Proposition 2.5 cannot be true in general since it implies disconnectedness, and there are connected Boolean Polish groups. The error comes from Axiom (O4) since it does not necessarily implies transitivy of the defined "order"