I am reading a proof on the generalization of Hensel's lifting lemma (over p-adic integers), particularly on 1-lipschitz functions. I came across a part with notations which I've never encountered before, hence I got confused.
Here are the important given for that part:
$\bullet M_k \subset \{0,1,2,...,p^k-1\} , k \geq1\\ \bullet h_i \in M_i \\ \bullet \mu \text{ is the set of all possible sequences } h_1, h_2,h_3,...,h_k \text{ where } h_k\in M_k $
And then the confusing part goes like this:
Since $$\lim_\gets M_k = \mu$$ and since $f$ is a continuous function,
then, $$f(a)= 0, \forall a \in \mu$$
I don't get the symbol with the limit with the left arrow, and how that implies to the conclusion shown.
I would appreciate if someone could make this clearer to me. Thank you!