Topology

Given a Set X a topology for X is a collection $\mathcal{T}$ of subsets of X with $\emptyset$ and X as elements, closed under unions and finite intersections. The members of $\mathcal{T}$ are called the Open Sets.

Topology also refers to the subject studying spaces with a topology defined as above. Such spaces are deemed topological spaces and their study is quite intoxicating.