%0 Journal Article %T Functional Space C(¦Ø), C0(¦Ø) %A Katuhiko Kanazashi %A Hiroyuki Okazaki %A Yasunari Shidama %J Formalized Mathematics %@ 1898-9934 %D 2012 %I %R 10.2478/v10037-012-0003-3 %X 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. %U http://versita.metapress.com/content/361n672t46816276/?p=430716bb19384440aaea6ce45ed7408d&pi=2