TopologicalSpace

A topological space is a set $X$ along with a collection of subsets of $X$, called the topology $\tau$, that satisfies specific properties. These subsets are known as open sets. The key properties of a topology are:

1. The empty set $\emptyset$ and the entire set $X$ are in $\tau$.
2. The union of any collection of sets in $\tau$ is also in $\tau$.
3. The intersection of any finite number of sets in $\tau$ is also in $\tau$.