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Hedgehog frames and a cardinal extension of normality
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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 Fσ-sublocales and invariant under closed maps.
Institution: DMUC 18-05
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