The topology induced by a topological space 
on a subset 
.
The open sets of 
are the intersections 
,
where 
is an open set of 
.
For example, in the relative topology of the interval ![S=[0,1]](/images/equations/RelativeTopology/Inline7.svg)
induced by the Euclidean
topology of the real line, the half-open interval
is open since it coincides with
![[0,1] intersection (-1,1/2)](/images/equations/RelativeTopology/Inline9.svg)
. This example
shows that an open set of the relative topology of 
need not be open in the topology of 
.
