Abstract
Our representation theorems are going to say that vector spaces provided with a certain algebraic structure (such as an ordering or a multiplication) are “isomorphic” with C(X) for some compact space X. 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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Groenewegen, G.L.M., van Rooij, A.C.M. (2016). Weak Topologies. The Alaoglu Theorem. In: Spaces of Continuous Functions. Atlantis Studies in Mathematics, vol 4. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-201-4_4
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DOI: https://doi.org/10.2991/978-94-6239-201-4_4
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Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-6239-200-7
Online ISBN: 978-94-6239-201-4
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