Analysis · Oct 6, 2026
Tingley’s sphere-isometry problem
Resolves Tingley's problem: every surjective isometry between the unit spheres of nonzero real Banach spaces extends uniquely to a surjective real-linear isometry of the whole spaces. No dimension restriction is imposed, so the metric geometry of the unit sphere determines the Banach space up to linear isometry.
Contributors
Unreleased OpenAI model
AI systems: Unreleased OpenAI model