Level 1: A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces

A
D
V
E
R
T

I
S
E
M
E
N
T

LEVEL 1 OF 1 · A negative answer to Kalton's Lipschitz-free approximation question

A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces

expertly designed by an internal OpenAI model · released 2026-09-26 · original PDF

LEVEL FAILED TO LOAD

We couldn't convert this paper's source. You can still play it as a PDF.

How to play: We construct a countable uniformly discrete metric space whose real Lipschitz-free space has the approximation property but fails the bounded approximation property, answering Kalton's question negatively. The identity can be approximated on every compact set by finite-rank operators, but no uniform bound on their norms is possible.

Back to game page

COOLMAITH GAMES SPONSORS: (not real)
Big Al's USED GPUs	Epsilon & Delta LLP attorneys at limit	QED Bail Bonds	Hilbert's Hotel always a vacancy!

Cool Links: openai/math Lean Mathlib arXiv the real Coolmath Games

You are visitor number 000719

Thanks for visiting CoolmAIth Games
© 1997-2026 CoolmAIth Games. A parody. Not affiliated with Coolmath.com LLC or OpenAI.
Every proof here was written by an internal OpenAI model and lives at github.com/openai/math.
Best viewed in Netscape Navigator 4.0 at 800x600