Title: There exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable
Abstract: We verify that there exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable in the sense that for given $s>1$, there is a nowhere Gevrey differentiable function on $\mathbb {R}$ of order $s$ that is Gevrey differentiable of order $r$ for any $r>s$, which also gives a strong example that is Gevrey differentiable but nowhere analytic.