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, 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.
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

Files in This Item:
File Description SizeFormat
TheLocalicHedgehog(FinalVersion)(Revised).pdf385.43 kBAdobe PDFView/Open
Show full item record

WEB OF SCIENCETM
Citations 10

2
checked on Oct 2, 2021

Page view(s)

53
checked on Oct 8, 2021

Download(s)

42
checked on Oct 8, 2021

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.