Subspace metric

This article describes the induced structure on any subset (subspace) corresponding to a particular structure on a set: the structure of a metric space
View other induced structures on subspaces

Definition

Suppose $(X,d_{X})$ is a metric space, and $Y\subseteq X$. The subspace metric on $Y$ is defined by simply restricting the metric on $X$ to points in $Y$. In other words, for $a,b\in Y$, we define $d_{Y}(a,b)=d_{X}(a,b)$.

Note that if we start with a geodesic metric space, the subspace metric on a subspace need not be a geodesic metric any more.