Definition 4.3:

The relation $\sim$ is said to be closed if $\Gamma$ is a closed subset of $X\times X$.

We shall employ the two projection maps

$$p:X\times X\longrightarrow X,\quad q:X\times X\longrightarrow X,$$

$$(x, y)\mapsto x,\phantom{XX}\quad (x, y)\mapsto y,\phantom{CC}$$

and denote by $\eta$ the quotient map $\eta : X \longrightarrow X/\sim$.