An algebraic scheme is semiseparated if it has a basis of topology by affine open subsets which is closed under finite intersections. Equivalently, the diagonal morphism is affine.
A cover of a scheme by affine open subsets is semiseparated (also spelled semi-separated, some say semiseparating or semi-separating) if is also affine for every pair .
A scheme is semiseparated iff it has an affine cover which is semiseparated.
An open subset of a semiseparated scheme is semiseparated.
Every semiseparated scheme is quasiseparated.
R. W. Thomason, T. Trobaugh: Higher algebraic K-theory of schemes and of derived categories, in: The
Grothendieck Festschrift* III, in: Progr. Math. 88, Birkhäuser (1990) 247–-435
L. Alonso Tarrío, A. Jeremías López, M. Pérez Rodríguez, María J. Vale Gonsalves; section 2 of: The derived category of quasi-coherent sheaves and axiomatic stable homotopy, Adv. Math. 218 4 (2008) 1224–-1252
A very short exposition is at the end of
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