Estimation of the muscle fiber density from the motor unit action potential

Abstract

A space $X$ has a $ mathbb{Q}$-diagonal if $X^2 setminus Delta$ has a $ mathcal{K}( mathbb{Q})$-directed compact cover. We show that any compact space with a $ mathbb{Q}$-diagonal is metrizable, hence any Tychonorff space with a $ mathbb{Q}$-diagonal is cosmic. These give a positive answer to Problem 4.2 and Problem 4.8 in cite{COT11} raised by Cascales, Orihuela and Tkachuk.