Definition:Compatible Quasiuniformities

Definition
Let $\UU_1$ and $\UU_2$ be quasiuniformities on a set $S$.

Let $\struct {\struct {S, \UU_1}, \tau_1}$ and $\struct {\struct {S, \UU_2}, \tau_2}$ be the quasiuniform spaces generated by $\UU_1$ and $\UU_2$.

Then $\UU_1$ and $\UU_2$ are compatible (with each other) their topologies are equal.

That is, $\tau_1 = \tau_2$.