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## Homework Statement

Let g belong to C([a,b]) be given, and let X={f belonging to C([a,b]) such that abs(f(t))<=abs(g(t)), for any t belonging to [a,b]}

Find all g's for which X is compact.

## Homework Equations

A compact set is closed and bounded. I believe that all the f's smaller tan g determine a bounded subset, as long as g is bounded. However, i dont understand so muc how can i put the closed part in. I believe that I need to work with the closure, as X will bo closed if X=cl(X), and cl(X)=all the f's smaller than g. However, im not able to put all this together, and to actually answer te question.

## The Attempt at a Solution

Any suggestion/hint, would be highly thanked.