Let A be a non-empty set in a metric space (X,d). Define by . Prove that f is continuous. I dont see how to bound f(x) and f(y)
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Hint The class of subsets of in the form or is a subbasis of . Prove that and are open sets.
Originally Posted by FGT12 Let A be a non-empty set in a metric space (X,d). Define by . Prove that f is continuous. Suppose that . or for each Thus or Can you continue to prove that
Originally Posted by Plato for each Thus How did you make this step? I understand that f(x)≤d(a,x), but how did you introduce f(y)?
Originally Posted by ILikeSerena How did you make this step? I understand that f(x)≤d(a,x), but how did you introduce f(y)? Note that or for each implies that is a lower bound for the set
Originally Posted by Plato Note that or for each implies that is a lower bound for the set Thanks! I got it now.
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