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i am studying from croom's introduction to topology book. i came across such a question. and i dont have a clue as to how to start .

Let X be a metric space with metric d and A a non-empty subset of X. define f:X->IR by :

f(x): d(x,A), x E X (x is an element of X)

show that f is continuous.

also if you can point out a solution book for this book that would be rather nice, considering i am computer scientist studying the topic at home..

thx.

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# Topology question - need help

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