Definition 5.3.9 (Equivalent Pseudometrics). Let $X$ be a set and $\seqi{d}, \seqj{d}$ be pseudometrics on $X$, then $\seqi{d}$ and $\seqj{d}$ are equivalent if their induced uniformities coincide.
Definition 5.3.9 (Equivalent Pseudometrics). Let $X$ be a set and $\seqi{d}, \seqj{d}$ be pseudometrics on $X$, then $\seqi{d}$ and $\seqj{d}$ are equivalent if their induced uniformities coincide.