Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43797
Title: Normal semicontinuity and the Dedekind completion of pointfree function rings
Authors: Gutiérrez García, Javier 
Mozo Carollo, Imanol 
Picado, Jorge 
Issue Date: 2016
Publisher: Springer
Issue Date: 2016
Publisher: Springer
Project: info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT 
Abstract: This paper supplements an earlier one by the authors which constructed the Dedekind completion of the ring of continuous real functions on an arbitrary frame L in terms of partial continuous real functions on L. In the present paper, we provide three alternative views of it, in terms of (i) normal semicontinuous real functions on L, (ii) the Booleanization of L (in the case of bounded real functions) and the Gleason cover of L (in the general case), and (iii) Hausdorff continuous partial real functions on L. The first is the normal completion and extends Dilworth’s classical construction to the pointfree setting. The second shows that in the bounded case, the Dedekind completion is isomorphic to the lattice of bounded continuous real functions on the Booleanization of L, and that in the non-bounded case, it is isomorphic to the lattice of continuous real functions on the Gleason cover of L. Finally, the third is the pointfree version of Anguelov’s approach in terms of interval-valued functions. Two new classes of frames, cb-frames and weak cb-frames, emerge naturally in the first two representations. We show that they are conservative generalizations of their classical counterparts.
URI: http://hdl.handle.net/10316/43797
Other Identifiers: 10.1007/s00012-016-0378-z
DOI: 10.1007/s00012-016-0378-z
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

Files in This Item:
File Description SizeFormat
Picado.pdf451.12 kBAdobe PDFView/Open
Show full item record

SCOPUSTM   
Citations

4
checked on Jun 25, 2019

WEB OF SCIENCETM
Citations

4
checked on Jun 25, 2019

Page view(s) 10

630
checked on Aug 20, 2019

Download(s)

22
checked on Aug 20, 2019

Google ScholarTM

Check

Altmetric

Altmetric


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