Which is the topology generated by the neighborhood system $V(x)=\{\{x\}\}$ My question is the following:
Which is the topology generated by the neighborhood system $V(x)=\{\{x\}\}$ ? 
I say that is the coarse topology but I don't know how is the mechanism to generate a topology from a basis
sorry if this is so trivial but I always have this doubt
thank you

By definition a set $U$ is open if and only if for every $x\in U$, there is a neighborhood $B_x\in V(x)$ such that $B_x\subset U$. Particularly, $V(x)\ni\{x\}\subseteq\{x\}$.. You should recognize that this is a standard topology on a set after some thought.
