Properties of the space of continuous functions on a closed interval
Mentor:Ivona Grzegorczyk, Professor of Mathematics, California State University Channel Islands
We study properties of the space of continuous functions on a closed interval [0,1] with respect to two metrics - d1 (f,g) = max |f(t)-g(t)| for all t and d2 = \int _0^1 |f-g| dt. We show examples of induced topology, inner products, norms, basis and Cauchy sequences. We will check if each space is separable, compact, complete, Banach, Hilbert. We will give proofs or show counter examples.