I have to show that $\mathbb{R},\mathcal{T}$ is a topology, where $\mathcal{T} = \{]-a,a[ \mid a > 0\} \cup \{\emptyset,\mathbb{R}\}$.
However, $\cup_{n \in \mathbb{N}} ]-2 + \frac{1}{n} , 2 -\frac{1}{n}[ = [-2,2]$which clearly is not an element in $\mathcal{T}$. Is the exercise faulty? Or am I missing something?