Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Philipp Hieronymi and I have recently established that if E is a boolean combination of open subsets of real euclidean n-space, and the expansion of the real field by E does not define the set of all integers, then the Lebesgue covering dimension of E is equal to its Assouad dimension (hence also to its Hausdorff and packing dimensions, and also to its upper Minkowski dimension if E is bounded). The proof is too technical to attempt in a seminar talk, but the result is surprisingly easy to prove for the case n=1. Indeed, I will prove the
(possibly) stronger result that all reasonable (in a way that I will make precise) Lipschitz invariant metric dimensions then coincide on E.
No Notes/Supplements Uploaded No Video Files Uploaded