Rigorous Proof of Dimension Properties for Kakeya Sets in Infinite-Dimensional Hilbert Spaces and 3D Euclidean Spaces Under the Pure ZFC Axiom System

Key Points

• The study aims to rigorously prove dimension properties for Kakeya sets within infinite-dimensional Hilbert spaces and 3D Euclidean spaces.
• Proof construction in the context of ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice) framework.
• Examination of mathematical properties relevant to Kakeya sets in high-dimensional spaces.
• Provides a definitive framework for understanding the dimension characteristics of Kakeya sets in infinite dimensions.
• Highlights potential implications for mathematical theories stemming from these properties.

Abstract