Every zero-dimensional homogeneous space is strongly homogeneous under determinacy.
2018
All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (that is, all its non-empty clopen subspaces are homeomorphic), with the trivial exception of locally compact spaces. In fact, we obtain a more general result on the uniqueness of zero-dimensional homogeneous spaces which generate a given Wadge class. This extends work of van Engelen (who obtained the corresponding results for Borel spaces) and complements a result of van Douwen.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
36
References
1
Citations
NaN
KQI