Topological Space

An ordered pair $(X, \tau)$, where $X$ is a set and $\tau$ is a collection of subsets of $X$ satisfying:

1. The empty set ($\emptyset$) and $X$ belong to $\tau$
2. Any arbitrary (in)finite union of members of $\tau$ still belongs to $\tau$
3. The intersection of any finite number of members of $\tau$ still belongs to $\tau$