Given $M=\{1,2,3,4\}$ find a topology on $M$ of minimum $3$ elements which makes $x=\{1,2,1,2,\dots\}$ converge. So, I've been having trouble with understanding this exercise:
It sounds like this:
Given $M=\{1,2,3,4\}$ find a topology on $M$ of minimum $3$ elements which makes $x=\{1,2,1,2,\dots\}$ converge.
I don't really understand what is $x$ supposed to be, and how to test it's convergence on the topology without a function.

You can take the  topology $\mathcal{T}=\{M, \emptyset\,\{1,2\}\}$ 
Use the definition of the convergence of a sequence in a topological space to see why this topology is a valid one.
