One of these sets is divided into simpler regions in Schwarz methods, which fall under a class (-5[1])of methods named for the “decomposition” of these sets. In complex analysis, either “region” or the word for this type of set also refers to a nonempty (10[1])open connected set. (10[1]-5[1])One of these sets (10[2])can be extended while preserving (10[1])a norm dominance (10[1])condition via the Hahn–Banach (10[1])theorem. (-5[1])In complex analysis, one of these sets is extended via analytic continuation. (10[2]-5[2])One (10[1])of these sets must be at least (10[1])as large (-5[1])as a related (10[1]-5[1])set for a surjection and no (-5[1])larger for an injection. (10[1]-5[2])In a common visualization, (-5[1])arrows point rightward from an oval (10[1])representing one of (10[1])these sets (10[2])to an oval (10[1])representing a related set prefixed (10[1])“co.” (10[6])For 10 (-5[1])points, (10[5])give this term (10[1])for the (10[1])set (10[2])of all inputs (10[1])to a function, (10[2])which (10[1])maps (10[1])to its range. (10[1])■END■ (10[16]0[1])