Show that for any metric space s if a sub s and x isin a a, Basic Statistics

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Show that for any metric space s if a sub s and x isin a a

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.

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Basic Statistics: Show that for any metric space s if a sub s and x isin a a

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