Question: Q1. Let x and Y be two normed vector spaces and let F:xY be an u.s.c set-valued mapping with compact values. Assume that x is

Q1. Let

x

and

Y

be two normed vector spaces and let

F:xY

be an\ u.s.c set-valued mapping with compact values. Assume that

x

is a compact space. Prove that

F(x)

is compact in

Y

Q1. Let X and Y be two normed vector spaces and let F:XY be an u.s.c set-valued mapping with compact values. Assume that X is a compact space. Prove that F(X) is compact in Y. (8 Marks)

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