Consider two metric spaces (X, dx) and (Y, dy). Show that if | X| is finite,...

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Consider two metric spaces (X, dx) and (Y, dy). Show that if | X| is finite, then there does not exist a function f : X → Y that is continuous. Prove that given metric spaces (X, dx), (Y, dy), (Z, dz), if ƒ : X → Y is contiu- ous at xo and g: Y→ Z is continuous at f(xo), then the composite function gof: X→ Z is continuous at xo. Consider two metric spaces (X, dx) and (Y, dy). Show that if | X| is finite, then there does not exist a function f : X → Y that is continuous. Prove that given metric spaces (X, dx), (Y, dy), (Z, dz), if ƒ : X → Y is contiu- ous at xo and g: Y→ Z is continuous at f(xo), then the composite function gof: X→ Z is continuous at xo.