It is well-known that the usual 'epsilon-delta' definition of continuity is equivalent to the sequential definition (assuming countable choice). Less well-known is the sequential definition of uniform continuity:
a function $f:[0,1] \rightarrow \mathbb{R}$ is sequentially uniformly continuous if for any sequences $(w_{n})_{n\in \mathbb{N}}$, $(v_{n})_{m\in \mathbb{N}}$ in $[0,1]$ such that $\lim_{n\rightarrow \infty}|w_{n}- v_{n}|=0$, we have $\lim_{n\rightarrow \infty}|f(x_{n}-f(y_{n})|=0$.
Are there (nice) sequential definitions of related classes, like Lipschitz or similer concept? I could not immediately find any.
