A question about topology regarding its conditions A question from a rookie.
As we know, $(X, T)$ is a topological space, on the following conditions,


*

*The union of a family of $T$-sets, belongs to $T$;

*The intersection of a FINITE family of $T$-sets, belongs to $T$;

*The empty set and the whole $X$ belongs to $T$.


So when the condition 2 is changed into:
2'. The intersection of a family of $T$-sets, belongs to $T$;
can anyone give a legitimate topological space as a counterexample to condition 2'?
Thank you.

The intersection of intervals $(-1/n,\ 1/n)$ for $n\in\mathbb N$ is only $\{0\}$ which is not open in $\mathbb R$ with the euclidean topology.
