Exercise 2, § 2

Soient X un B-space et R une relation d’équivalence sur X.

(a) Prove that the relation R is compatible with the structure of B-space on X if and only if its graph is contained in $X\times_BX$.

(b) In this case, prove that the canonical mapping $X/R\rightarrow B$ is separated if and only if the graph of R is closed in $X\times_BX$.