期刊
JOURNAL OF SYMBOLIC LOGIC
卷 87, 期 2, 页码 732-757出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jsl.2020.52
关键词
Borel hierarchy; Wadge hierarchy; fine hierarchy; iterated labeled tree; h-quasiorder; better quasiorder; Q-partition
类别
资金
- RFBR-JSPS [20-51-50001]
The Wadge hierarchy, originally defined and studied in the Baire space, has been extended to arbitrary topological spaces by providing a set-theoretical definition of all its levels. The extension behaves well in second countable spaces and especially in quasi-Polish spaces. The levels are preserved by continuous open surjections between second countable spaces, leading to several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces.
The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). Here we extend the Wadge hierarchy of Borel sets to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces which implies e.g., several Hausdorff-Kuratowski (HK)-type theorems in quasi-Polish spaces. In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据