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Title: Hedgehog frames and a cardinal extension of normality
Authors: Gutiérrez García, Javier
Mozo Carollo, Imanol
Picado, Jorge 
Walters-Wayland, Joanne
Keywords: Frame, locale, frame of reals, metric hedgehog frame, metrizable frame, weight of a frame, separating family of localic maps, universal frame, join cozero \kappa-family, normal frame, \kappa-collectionwise normal frame, closed map
Issue Date: 2019
Publisher: Elsevier
Project: UID/MAT/00324/2013 
Serial title, monograph or event: Journal of Pure and Applied Algebra
Volume: 223
Issue: 6
Abstract: The hedgehog metric topology is presented here in a pointfree form, by specifying its generators and relations. This allows us to deal with the pointfree version of continuous (metric) hedgehog-valued functions that arises from it. We prove that the countable coproduct of the metric hedgehog frame with κ spines is universal in the class of metric frames of weight \kappa⋅\aleph_0. We then study \kappa-collectionwise normality, a cardinal extension of normality, in frames. We prove that this is the necessary and sufficient condition under which Urysohn separation and Tietze extension-type results hold for continuous hedgehog-valued functions. We show furthermore that \kappa-collectionwise normality is hereditary with respect to F_\sigma-sublocales and invariant under closed maps.
DOI: 10.1016/j.jpaa.2018.08.001
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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