Abstract
Paracompactness behaves in the point-free context better than in the classical one. It has all the properties known from spaces (full normality, various characteristics by the properties of covers, see 2.3.4), and it is implied by metrizability. But we also have a very pleasing fact that a frame is paracompact iff it admits a complete uniformity (which is not true in the classical case), and this in turn, very much in contrast with the classical situation, yields the reflectivity of paracompact locales in the general ones (making them closed under limit constructions).
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© 2012 Springer Basel AG
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Picado, J., Pultr, A. (2012). Paracompactness. In: Frames and Locales. Frontiers in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0154-6_9
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DOI: https://doi.org/10.1007/978-3-0348-0154-6_9
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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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