Sequence of functions and its graph

104 Views Asked by Bumbble Comm At 23 Feb 2026 - 10:43

Consider a sequence of functions f_n in C⁰. Suppose G_n of f_n is a compact subset of R².

Then prove f_n converges uniformly as n-> ∞ if and only if the sequence G_n in K(R²) converges to the graph of the function f in C⁰.

I know we have to use Arzela-Ascoli but i don't know how to apply it. Can anyone help?