If $g(t)$ is Ricci flow on $[0,T)$, and $$ |Rm|\le M ~~~~~~ \forall t\in[0,T), $$ By the Metric equivalence $$ e^{-2Mt} g(0) \le g(t)\le e^{2Mt} g(0), $$ I know $g(t)$ is bounded (namely, there is $A,B\ge0$ such that $A|\epsilon|^2\le g(\epsilon, \epsilon)\le B|\epsilon|^2$). Topping state that $g(t)$ can be extended continuously to $[0,T]$. But in my view, bounded function may not be extended continuously, for example $$ f(x)=\sin\frac{1}{x} $$ is bounded on (0,1], but it can't be extended continuously to $[0,1]$. Of course, I don't know the case of tensor.
Since my English is poor, I add some picture of Topping's Lectures on the Ricci flow against that I misunderstand it.
