%0 Journal Article %T Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support %A Katuhiko Kanazashi %A Noboru Endou %A Yasunari Shidama %J Formalized Mathematics %@ 1898-9934 %D 2010 %I %R 10.2478/v10037-010-0002-1 %X In this article, we give a definition of a functional space which is constructed from all 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 real-valued continuous functions with bounded support. We prove that this function space is a real normed space. %U http://versita.metapress.com/content/l16qq2287453l826/?p=61b23553b62540b9a78312c2f3ea4bb9&pi=1