Let (X,d) a metric space. Show that the function y↦d(x,y) is continuous. Please help me, I don't know where to start.
2026-04-06 16:32:50.1775493170
Let (X,d) a metric space. Show that a function is continuous
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$d(x,y) \leq d(x,y')+d(y,y')$ and $d(x,y') \leq d(x,y)+d(y,y')$. Combine these to get $|d(x,y)-d(x,y')| \leq d(y,y')$.