11. Define g: l2 → R by g(x) = En-1 n/n, where x = (x₁, x2,...). True or false: the map g is continuous. 12. Let VX be a closed subset of X and x € X\V be a point. Prove that there exist disjoint open sets A and B such that x EA and VC B. Can A and B be chosen such that A and B are disjoint.

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11. Define g: l2 → R by g(x) = -1 n/n, where x = (x1, x2,...). True or false: the map g
is continuous.
12. Let VX be a closed subset of X and x € X\V be a point. Prove that there exist disjoint
open sets A and B such that x EA and VC B. Can A and B be chosen such that A and
B are disjoint.
Transcribed Image Text:11. Define g: l2 → R by g(x) = -1 n/n, where x = (x1, x2,...). True or false: the map g is continuous. 12. Let VX be a closed subset of X and x € X\V be a point. Prove that there exist disjoint open sets A and B such that x EA and VC B. Can A and B be chosen such that A and B are disjoint.
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