Question: Let I := [a, b] and let f : I R be a (not necessarily continuous) function with the property that for every x

Let I := [a, b] and let f : I → R be a (not necessarily continuous) function with the property that for every x ∈ I, the function f is bounded on a neighborhood Vδx (x) of x (in the sense of Definition 4.2.1). Verify that f is bounded on I.

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