# Is [0,1] Closed at the Origin?

Please solve the following problem:

Let C ([0,1]) be the space of continuous functions in [0,1] with the norm

II f II = max I f(x) I on [0,1].

Is the subspace of functions that are = 0 at the origin closed subspace in

C^0 [o,1] with this norm/Prove or disapprove.

https://brainmass.com/math/analytic-geometry/closed-origin-381089

#### Solution Preview

Yes, it is closed. Suppose, {f_n} is a sequence of functions from the subspace Y={g in C([0,1]): g(0)=0} converging to some function f in C([0,1]) in ...

#### Solution Summary

The solution proves or disapproves if [0,1] closed at the origin.

$2.19