<Reference List> | |
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 |
Online version: | http://www.mat.uc.pt...prints/eng_2018.html |
Download: | Not available |