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.