Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/90471
 Title: Hedgehog frames and a cardinal extension of normality Authors: Gutiérrez García, JavierMozo Carollo, ImanolPicado, 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. URI: http://hdl.handle.net/10316/90471 DOI: 10.1016/j.jpaa.2018.08.001 Rights: embargoedAccess Appears in Collections: I&D CMUC - Artigos em Revistas Internacionais

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