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]](https://txtdot.deep-swarm.xyz/proxy/img?url=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FRelativeTopology%2FInline7.svg){kind=small}
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)](https://txtdot.deep-swarm.xyz/proxy/img?url=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FRelativeTopology%2FInline9.svg){kind=small}
. This example
shows that an open set of the relative topology of 
need not be open in the topology of 
.
This entry contributed by Margherita Barile
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Cite this as:
Barile, Margherita. "Relative Topology." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RelativeTopology.html