Topological space

               Topology: Definition:

  Topological Space:

Given a set , a topology  on  is a collection of subsets of  (called open sets) with the following properties:

• The empty set and  are both in .
• The union of any collection of open sets is an open set. That is, .
• The intersection of any finite collection of open sets is an open set. That is, .

The pair  is called a topological space. If the topology is clear or does not need an explicit name (since we can just refer to sets in the topology as open sets), then we just say that  is a topological space.