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## Homework Statement

Dn={f in C([0,1]) : there exists t in [0,1] for every h in R/{0}, abs((f(t+h)-f(t))/h) <=n}

prove the Dn's are closed nowhere dense sets. A subset of some set A is closed in A if its complement is open in A.

## Homework Equations

## The Attempt at a Solution

i first defined the complement of Dn as the set in which for all t in [0,1], abs((f(t+h)-f(t))/h)>n. Is trying to prove closed first and then nowhere dense.