Elementary topology and machine learning

The machine learning bubble may be overinflated, but it is not about to burst. Interdisciplinary research in this field is grounded in sound theory and has numerous empirical breakthroughs to show for. As it finds more and more applications and concentrates public research funding, many of us are still wondering: how can mathematics contribute?
Case study of an interaction between elementary topology and machine learning’s binary classification problem. Following classical theorems, we obtain a topologically accurate solution.

Correction: It should be $\sup_{i,j}| E_{i,j}^n - (k+1)^2 \int_{R_{i,j}^n} f | = o(1/n)$ and $k=k(n)$ grow correspondingly slower with $n$.

PDF note here.