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Prove the following:
Theorem. Let
[Hint: If
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Topology
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- let (X,T) be a topological space. Then a function f is continuous at x0 element of X if and only if f is both lower semi continuous and upper semi continuous at x0 element of X.arrow_forwardLet A and B be topological spaces and endow A x B and B X A with respective product topologies. Show that the map f: A × B → B × A defined by f(a, b) = (b, a) is a homeomorphism.arrow_forward
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