Let X be a metric space and x0 in X. Define a function f: X --> R (all real numbers) by f(x) = d(x,x0). Show that f is continuous.
HINT: Prove the variant of the triangle inequality which says
|d(x,z)-d(y,z)|< d(x,y) for any x,y,z in X
This show show to prove a function in a metric space is continuous.