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 \(\tau\)