Please use this identifier to cite or link to this item:
https://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 | Serial title, monograph or event: | Forum Mathematicum | Volume: | 27 | Issue: | 5 | 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: | https://hdl.handle.net/10316/43901 | DOI: | 10.1515/forum-2012-0095 10.1515/forum-2012-0095 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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File | Description | Size | Format | |
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forum0095.pdf | 323.72 kB | Adobe PDF | View/Open |
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