Titlebook: Spaces of Continuous Functions; G.L.M. Groenewegen,A.C.M. van Rooij Book 2016 Atlantis Press and the author(s) 2016 Spaces of Continuous F

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https://doi.org/10.2991/978-94-6239-201-4Spaces of Continuous Functions; Compact Hausdorff Spaces; Riesz Spaces; Representation Theorems; Weak To

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The Stone-Weierstrass Theorem,ximated uniformly by polynomial functions. We prove an extension of this result. The theorem itself lies outside our sphere of interest, but it is crucial for the representation theorems in our later chapters.

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Weak Topologies. The Alaoglu Theorem,are “isomorphic” with .(.) for some compact space .. To obtain such a result we must conjure up compact spaces. Our magic want will be the Alaoglu Theorem, itself a consequence of the Tychonoff Theorem. The basic idea is the following.

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Book 2016 theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem..The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory..