Let (X,d) a metric space. Show that a function is continuous

Question

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.

Start off by writing the definitions. – 5xum Feb 19 '19 at 09:21 — 5xum, Feb 19 '19 at 09:21

score 1 · Answer 1 · answered Feb 19 '19 at 09:21

1

$d(x,y) \leq d(x,y')+d(y,y')$ and $d(x,y') \leq d(x,y)+d(y,y')$. Combine these to get $|d(x,y)-d(x,y')| \leq d(y,y')$.

answered Feb 19 '19 at 09:21

Kavi Rama Murthy

1 Answers1