Abstract
In order to prove that the continuous subalgebra does not have the Kadison-Singer property, we construct the Stone-Čech compactification of Tychonoff spaces. We do this by discussing the notion of ultrafilters for meet-semilattices. We show that we can topologize the set of ultrafilters on the zero-sets of a Tychonoff space in such a way that this set becomes the Stone-Čech compactification, which we prove in full detail.
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Stevens, M. (2016). Stone-Čech Compactification. In: The Kadison-Singer Property. SpringerBriefs in Mathematical Physics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-47702-2_6
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DOI: https://doi.org/10.1007/978-3-319-47702-2_6
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47701-5
Online ISBN: 978-3-319-47702-2
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