Consider $X:=[0,\infty)$, equipped with the topology generated by intervals of the form $[a,+\infty)$, $a\geq 0$. In my topology text this is called the Arrow topology but I think this is nonstandard.
We wish to determine $\text{Int}[0,1]$. My conjecture is that it is $\varnothing$, since no open set is contained in $[0,1]$. Is this argument correct? It feels unusual to say the interior is empty with such a "nonempty" set.
Best Answer
The argument is almost correct. The interior of $[0,1]$ is empty because $\emptyset$ is the only open subset of $[0,1]$.