Topological Spaces on Three Points
A topological space can be defined as a pair , where is a set of points and (a topology) is a collection of subsets of called open that satisfy four conditions:[more]
1. The empty set and the set itself belong to .
2. Any finite or infinite union of members of also belongs to .
3. The intersection of any finite number of members of also belongs to .
Topological spaces are, of course, usually associated with infinite sets of points. But it is amusing to apply topology to a finite set of points. This Demonstration considers a space , with selected from the power set of three points: , , , , , , and . The set is a topological space only if the three conditions listed are satisfied.[less]
Snapshot 1: fulfills the condition for a topology
Snapshot 2: is not a topology, since the subset is missing
Snapshot 3: is not a topology, since the element is missing
 Wikipedia. "Topological Space." (May 11, 2018) en.wikipedia.org/wiki/Topological_space.