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Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

DOI: 10.2478/v10037-010-0002-1

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Abstract:

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.

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