Continuous images of closed sets in generalized Baire spaces
Continuous images of closed sets in generalized Baire spaces
复制标题
广义贝尔空间中闭集的连续图像
DOI：
10.1007/s11856-015-1224-2
复制
发表时间：
2015
影响因子：
1
通讯作者：
Philipp Schlicht
中科院分区：
文献类型：
--
作者：
Philipp Lücke;Philipp Schlicht
设k是不可数基数，给定一个基数μ，我们为由从k到μ的所有函数组成的集合配备一个拓扑，该拓扑的基本开集由基数小于k的部分函数的所有扩展组成。我们证明的结果，使我们能够分离的几个类的子集，包括连续图像的闭子集的空间的形式。这类结果的重要例子如下：（i）存在的闭子集，它不是的连续像;（ii）存在的内射连续像，它不是κ-Borel（即，不包含在最小集合代数中的集合（包含所有开子集并且在κ-并下是闭的）;（iii）陈述“的每个连续像是的闭子集的内射连续像”独立于ZFC的公理;（iv）ZFC的公理并不证明假设“”蕴涵陈述“的每个闭子集是的连续像”或其否定。
Letκbe an uncountable cardinal with. Given a cardinal µ, we equip the setconsisting of all functions fromκtoμwith the topology whose basic open sets consist of all extensions of partial functions of cardinality less thanκ. We prove results that allow us to separate several classes of subsets ofthat consist of continuous images of closed subsets of spaces of the form. Important examples of such results are the following: (i) there is a closed subset ofthat is not a continuous image of; (ii) there is an injective continuous image ofthat is notκ-Borel (i.e., that is not contained in the smallest algebra of sets onthat contains all open subsets and is closed underκ-unions); (iii) the statement “every continuous image ofis an injective continuous image of a closed subset of” is independent of the axioms of ZFC; and (iv) the axioms of ZFC do not prove that the assumption “” implies the statement “every closed subset ofis a continuous image of” or its negation.
影响因子：
0.6
作者：
Luecke, Philipp
通讯作者：
Luecke, Philipp