Southern California Conferences for Undergraduate Research

Southern California Conferences for Undergraduate Research

Properties of the space of continuous functions on a closed interval

Author:

Lucas Mattick

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.


Presented by:

Lucas Mattick

Date:

Saturday, November 17, 2012

Poster:

85

Room:

Broome Library

Presentation Type:

Poster Presentation

Discipline:

Mathematics
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