Round 3: Tossup 16

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. One of these sets can be extended while preserving (10[1])a norm dominance condition via the Hahn–Banach (10[1])theorem. In complex analysis, one of these sets is extended via analytic continuation. One of these sets must be at least as large (-5[1])as a related set for a surjection and no larger for an injection. In a common visualization, arrows point rightward from an oval (10[1])representing one of these sets (10[1])to an oval representing a related set prefixed “co.” (10[3])For 10 (-5[1])points, give this term for the set of all inputs to a function, which maps to its range. ■END■ (10[2])

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