State the principle of uniform boundedness. Use it to show that a set E in a normed space X is bounded if )E(f is bounded in K for every f ∈ X′.

The principle of uniform boundedness, also known as the Banach-Steinhaus theorem, is a fundamental result in functional analysis. It states that if a family of continuous linear operators from a normed space \(X\) to a Banach space \(Y\) is ______ ___ __________ ______ __________ _________.
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