Open set of real valued functions

[rjw5002]

Homework Statement

Consider the set X = {f:[0,1] \rightarrow R | f \in C[0,1]} w/ metric d(f,g) = sup|f(x) - g(x)| (x \in [0,1])
Prove that the set A = {f \in X | f(0) > 1} is open in (X,d).

Homework Equations

E is open if every point of E is an interior point
p is an interior point of E if there is a neighborhood N of p s.t. N\subsetE.
C[0,1] is the set of all real valued functions on [0,1]
supremum.

The Attempt at a Solution

To be honest, I have a great deal of difficulty understanding this question. Any hints or advice to help me in the right direction would be greatly appreciated.

 

[HallsofIvy]

If f is a function in A what does a neigborhood of A look like?

If A is the set of all functions, f, such that f(0)> 1, what are the interior points of A?