Topological Spaces
Definition
The pair is a topological space. Elements of are called open sets.
Examples
Example 1: Discrete topology: (all subsets are open).
Example 2: Indiscrete topology: (only trivial open sets).
Example 3: Standard topology on : open intervals generate the topology.
Example 4: Finite complement topology: is open if is finite or .
Basis for a Topology
The topology generated by consists of all unions of elements of .