Consider to be a non-empty set, and also let
be a subset of the power set of , such that an action fullfils the following conditions,
- ,
- if then also the finite intersetion of these sets are element of the topology, i.e.
- .
- let be an index set and for all the subset is element of the topology ( ) then also the union of these sets is an element of the topology <\math>, i.e.
- .
The pair is called topological space.
Set sets in are called the open sets in .
- Let and . Add a minimal number of sets, so and create , so that is a topological space.