Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Hedgehog frames and a cardinal extension of normality
Publication Date:	2018-01-31
Authors:	- Javier Gutiérrez García - Imanol Mozo Carollo - Jorge Picado - Joanne Walters-Wayland
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 κ·ℵ₀. We then study κ-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 κ-collectionwise normality is hereditary with respect to F_σ-sublocales and invariant under closed maps.
Institution:	DMUC 18-05
Online version:	http://www.mat.uc.pt...prints/eng_2018.html
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