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.
@article{bwmeta1.element.doi-10_2478_v10037-010-0002-1,
author = {Katuhiko Kanazashi and Noboru Endou and Yasunari Shidama},
title = {Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support},
journal = {Formalized Mathematics},
volume = {18},
year = {2010},
pages = {11-16},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0002-1}
}
Katuhiko Kanazashi; Noboru Endou; Yasunari Shidama. Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support. Formalized Mathematics, Tome 18 (2010) pp. 11-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0002-1/
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