Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43901
Title: On the Dedekind completion of function rings
Authors: Mozo Carollo, Imanol 
Gutiérrez García, Javier 
Picado, Jorge 
Issue Date: 2015
Publisher: De Gruyter
Project: PEst-C/MAT/UI0324/2011 
Abstract: This paper introduces the frame of partially defined real numbers and the lattice-ordered ring of partial real functions on a frame. This is then used to construct the order completion of rings of pointfree continuous real functions. The bounded and integer-valued cases are also analysed. The application of this pointfree approach to the classical case C(X) of the ring of continuous real-valued functions on a topological space X yields a new construction for the Dedekind completion of C(X), considerably more direct and natural than the known procedure using Hausdorff continuous functions.
URI: http://hdl.handle.net/10316/43901
Other Identifiers: 10.1515/forum-2012-0095
DOI: 10.1515/forum-2012-0095
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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