(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the set X = {f:[0,1] [tex]\rightarrow[/tex] R | f [tex]\in[/tex] C[0,1]} w/ metric d(f,g) = sup|f(x) - g(x)| (x [tex]\in[/tex] [0,1])

Prove that the set A = {f [tex]\in[/tex] X | f(0) > 1} is open in (X,d).

2. Relevant 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[tex]\subset[/tex]E.

C[0,1] is the set of all real valued functions on [0,1]

supremum.

3. 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.

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# Homework Help: Open set of real valued functions

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