Partitions of 2ω and completely ultrametrizable spaces

We prove that, for every n, the topological space ωnω (where ωn has the discrete topology) can be partitioned into ℵn copies of the Baire space. Using this fact, we then prove two new theorems about completely ultrametrizable spaces. We say that Y is a condensation of X if there is a continuous bije...

Full description

Saved in:
Bibliographic Details
Published in:Topology and its applications 2015-04, Vol.184, p.61-71
Main Authors: Brian, William R., Miller, Arnold W.
Format: Article
Language:English
Subjects:
Borel set
Completely ultrametrizable spaces
Condensation
Partition
Similarity relation
Tree
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that, for every n, the topological space ωnω (where ωn has the discrete topology) can be partitioned into ℵn copies of the Baire space. Using this fact, we then prove two new theorems about completely ultrametrizable spaces. We say that Y is a condensation of X if there is a continuous bijection f:X→Y. First, it is proved that ωω is a condensation of ωnω if and only if ωω can be partitioned into ℵn Borel sets, and some consistency results are given regarding such partitions. It is also proved that it is consistent with ZFC that, for any n
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2015.01.014