Definition 6.4.7 (Cauchy Continuous).label Let $X, Y$ be uniform spaces and $f: X \to Y$, then $f$ is Cauchy continuous if for any Cauchy filter base $\fB \subset 2^{X}$, $f(\fB) \subset 2^{Y}$ is Cauchy.
Definition 6.4.7 (Cauchy Continuous).label Let $X, Y$ be uniform spaces and $f: X \to Y$, then $f$ is Cauchy continuous if for any Cauchy filter base $\fB \subset 2^{X}$, $f(\fB) \subset 2^{Y}$ is Cauchy.