What is the intersection of the sets ${1}$ and ${1,2}$?
For me, it would make sense that ${1} cap {1,2} = 1$, but I’m afraid it must be ${1}$, otherwise for instance $T = { {}, {1}, {1,2} }$ would not be a topology of $X = {1,2}$ since $1$ does not belong to $T$.
What is the reason that ${1} cap {1,2}$ could not be $1$?