Abstract
In this chapter, we present some of the interactions between the theories of uniform spaces and rings of continuous functions. We shall find that every realcompact space admits a complete structure. One of the outstanding successes of the theory of rings of continuous functions is Shirota’s result that, barring measurable cardinals, the converse is also true, so that the spaces admitting complete structures are precisely the realcompact spaces.
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© 1960 D. Van Nostrand Company, Inc.
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Gillman, L., Jerison, M. (1960). Uniform Spaces. In: Rings of Continuous Functions. The University Series in Higher Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7819-2_15
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DOI: https://doi.org/10.1007/978-1-4615-7819-2_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90120-6
Online ISBN: 978-1-4615-7819-2
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