# Topological Space

##### Updated: October 21, 2020

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

- The empty set (\(\emptyset\))
**and**\(X\) belong to \(\tau\) - Any arbitrary (in)finite union of members of \(\tau\) still belongs to \(\tau\)
- The intersection of any
*finite*number of members of \(\tau\) still belongs to \(\tau\)