A short note on hereditary Mazur intersection property
Pradipta Bandyopadhyay, Deepak Gothwal
TL;DR
This paper demonstrates that the hereditary Mazur intersection property (MIP) does not necessarily lead to Fréchet smoothness, providing a counterexample to clarify their relationship.
Contribution
It establishes that hereditary MIP does not imply Fréchet smoothness, clarifying the limitations of the property with a specific example.
Findings
Hereditary MIP does not imply Fréchet smoothness.
Provides a counterexample by Borwein and Fabian (1993).
Clarifies the relationship between MIP and smoothness.
Abstract
In this note, we prove that hereditary Mazur intersection property (MIP) does not imply Fr\'echet smoothness using an example by Borwein and Fabian (1993).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPoint processes and geometric inequalities · Medical Image Segmentation Techniques · Topological and Geometric Data Analysis