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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 20, Issue 1


Functional Space C(ω), C0(ω)

Katuhiko Kanazashi / Hiroyuki Okazaki / Yasunari Shidama
Published Online: 2012-09-12 | DOI: https://doi.org/10.2478/v10037-012-0003-3

Functional Space C(ω), C0(ω)

In this article, first we give a definition of a functional space which is constructed from all complex-valued continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.

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About the article

Published Online: 2012-09-12

Published in Print: 2012-01-01

Citation Information: Formalized Mathematics, Volume 20, Issue 1, Pages 15–22, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0003-3.

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