Infinite-Dimensional Kakeya Sets with Finite Hausdorff Dimension Finite-Dimensional Direction Spanning Subspace

Key Points

• The aim is to investigate the characteristics of infinite-dimensional Kakeya sets alongside their finite Hausdorff dimension.
• Theoretical analysis of geometric properties of Kakeya sets.
• Mathematical modeling and proofs regarding dimension and spanning subspaces.
• Infinite-dimensional Kakeya sets exhibit properties that are not intuitive from finite dimensions.
• Finite Hausdorff dimension is demonstrated under specific geometric configurations.

Abstract