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Title: | A general insertion theorem for uniform locales | Authors: | Arrieta, Igor Avilez, Ana Belén |
Keywords: | Locale; Frame; Cover; Insertion theorem; Extension theorem; Separation theorem | Issue Date: | 2023 | Publisher: | Elsevier | Serial title, monograph or event: | Journal of Pure and Applied Algebra | Volume: | 227 | Issue: | 7 | Abstract: | A general insertion theorem due to Preiss and Vilimovský is extended to the category of locales. More precisely, given a preuniform structure on a locale we provide necessary and sufficient conditions for a pair f≥gof localic real functions to admit a uniformly continuous real function in-between. As corollaries, separation and extension results for uniform locales are proved. The proof of the main theorem relies heavily on (pre-)diameters in locales as a substitute for classical pseudometrics. On the way, several general properties concerning these (pre-)diameters are also shown. | URI: | https://hdl.handle.net/10316/112642 | ISSN: | 00224049 | DOI: | 10.1016/j.jpaa.2023.107320 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
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A general insertion theorem for uniform locales.pdf | 506.96 kB | Adobe PDF | View/Open |
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