Answer to Question #15451 in Real Analysis for ran

Question

Let X and Y be metric spaces and let f:=X→Y be a mapping. Pick out the true statements:

a. if f is uniformly continuous, then the image of every Cauchy sequence in X is a Cauchy sequence in Y ;

b. if X is complete and if f is continuous, then the image of every Cauchy sequence in X is a Cauchy sequence in Y ;

c. if Y is complete and if f is continuous, then the image of every Cauchy sequence in X is a Cauchy sequence in Y