Metric embeddings of cubes into dense subsets of cubes

Miltiadis Karamanlis, Cosmas Kravaris

Fix $k\in \mathbb{N},0<\delta <1$. We study how large $N$ must be so that every $\delta$-dense subset $\mathcal{D}\subset \{0,1{\}}^N$ (meaning $|\mathcal{D}|\ge \delta 2^N$) contains the imag…