Let [math]X[/math] be any set. Then the power set of [math]X[/math] is denoted by [math]\mathcal{P}(X)[/math], and it is the set of all subsets of [math]X[/math].
A topology on [math]X[/math] is a special kind of subset of its power set.
Let [math]\mathcal{T}\subseteq\mathcal{P}(X)[/math].
Then [math]\mathcal{T}[/math] is a topology on [math]X[/math]...