Abstract
We have alreadymentioned that metrizability was defined by Isbell as the existence of a countably generated (admissible) uniformity. In this chapter we will show that in such a case there is indeed a diameter function with the properties mimicking those of the diameter in a classical metric space. We show a link of thus ensuing metric frames with metric spaces by a specialized spectrum adjunction, present metrization theorems extending those of the classical theory, and, finally, discuss the resulting categories.
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© 2012 Springer Basel AG
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Picado, J., Pultr, A. (2012). Metric Frames. In: Frames and Locales. Frontiers in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0154-6_11
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DOI: https://doi.org/10.1007/978-3-0348-0154-6_11
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0153-9
Online ISBN: 978-3-0348-0154-6
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