# Subspace

Let $(X,\tau)$ be a topological space, $Y \subset X$, and define $\tau_Y = \{ Y \cap Z \colon Z \in \tau\}$. We say that the ordered pair $(Y,\tau_Y)$ is the subspace topological space associated with $Y$ and we say that $\tau_Y$ is the subspace topology associated with $Y$.