Subspace topology
In topology and related areas of mathematics, a subspace of a topological space ( X , τ ) {\displaystyle (X,\tau )} is a subset S of X which is equipped with a topology induced from that of τ {\displaystyle \tau } called the subspace topology (or the relative topology, inherited topology, induced topology, or trace topology). == Definition == Given a topological space ( X , τ ) {\displaystyle (X,\tau )} and a subset S {\displaystyle S} of X {\displaystyle X} , the subspace topology on S {\displaystyle S} is defined by τ S = { S ∩ U ∣ U ∈ τ } .