Hi, can someone give me pointers on this question 1. The problem statement, all variables and given/known data Prove or provide a counterexample: If f : E -> Y is continuous on a dense subset E of a metric space X, then there is a continuous function g: X -> Y such that g(z) = f(z) for all z element of E. 3. The attempt at a solution I'm not sure if the statement is true or not. I have tried to find counter-examples using continuous functions on the rationals or irrationals. For example f: Q -> R , f(x) = x. This is continuous for every x in Q. However it is easy to find a mapping g: R -> R which is continuous and g(z) = f(z) for all z element of Q. ie given by g(x) = x. I am yet to find a counter-example (in R anyway). However if the statement holds I'm not to sure how I would begin to prove it. Thanks!