Continuous real-valued function

Reference no: EM13966727

Show that for any metric space S, if A ⊂ S and x ∈ A\ A, then there is a bounded, continuous real-valued function on A which cannot be extended to a function continuous on A∪{x }. Hint: f (t ) := sin(1/t ) for t > 0 cannot be extended continuously to t = 0.

Reference no: EM13966727

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