Let be the space of continuous functions with norm || . I am trying to determine whether the linearly independent set is dense in Somebody gave me a hint that it is not dense and to look at the constant function 1. So that means I am trying to show that there is some open ball around the function 1, which contains no element of .

This means that I need to show for some 0.

Has anyone got any hints regarding how to go about this? Thanks very much