Definition 5.1.5 (Subspace Uniformity). Let $(X, \fU)$ be a uniform space and $A \subset X$, then the family
\[\fU_{A} = \bracs{U \cap (A \times A)| U \in \fU}\]
forms a uniformity on $A$, known as the subspace uniformity induced on $A$.
Definition 5.1.5 (Subspace Uniformity). Let $(X, \fU)$ be a uniform space and $A \subset X$, then the family
forms a uniformity on $A$, known as the subspace uniformity induced on $A$.