What is a cube?
Tuomas Hyt\"onen, Anna Kairema
TL;DR
This paper provides an intrinsic characterization of subsets in doubling metric spaces that can be represented as dyadic cubes, clarifying the structure of such partitions in metric space analysis.
Contribution
It offers a new intrinsic criterion for identifying dyadic cube subsets in doubling metric spaces, extending Christ's construction.
Findings
Characterization of dyadic cube subsets in doubling metric spaces
Extension of Christ's dyadic cube construction
Clarification of the structure of dyadic partitions
Abstract
We give an intrinsic characterization of all subsets of a doubling metric space that can arise as a member of some system of dyadic cubes on the underlying space, as constructed by M. Christ.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Fixed Point Theorems Analysis · Advanced Banach Space Theory