Separatedness is the algebraic-geometric analogue of the T2-space condition. It is preserved by composition and base change.
Every proper morphism is separated.
Grothendieck, A. and Dieudonné, J. "Éléments de géométrie algébrique. II. Étude globale élémentaire
de quelques classes de morphismes." Publ. Math. IHES8, 5-222,
1961. https://doi.org/10.1007/BF02699291.The
Stacks Project Authors. "Separation Axioms." §26.21 in The Stacks
Project, Tag 01KH, 2026. https://stacks.math.columbia.edu/tag/01KH.
of schemes whose diagonal
morphism 
is a closed immersion.
