Abstract
We give three examples of metric spaces where the inductive dimensions disagree. The two main examples are both N-compact. The first has closed sets which are not clopen Borel (Borel in the σ-algebra generated by the clopen sets). The second has weight ω 1 and, assuming all sets of cardinality ω 1 in the interval are Q-sets, contrasts the first by having all closed sets clopen Borel. The third example provides, for each α with ω 1⩽α⩽ c , a metric space of weight α with noncoinciding dimensions for which all subsets of weight less than α are strongly zero-dimensional. Each example answers a question posed by Mrowka.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
