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https://hdl.handle.net/10316/4615
Title: | A new look at localic interpolation theorems | Authors: | Picado, Jorge | Keywords: | Locales; Normal frames; Frame of reals; Upper (lower) frame of reals; Continuous real functions; Upper (lower) semicontinuous real functions | Issue Date: | 2006 | Citation: | Topology and its Applications. 153:16 (2006) 3203-3218 | Abstract: | This paper presents a new treatment of the localic Katetov-Tong interpolation theorem, based on an analysis of special properties of normal frames, which shows that it does not hold in full generality. Besides giving us the conditions under which the localic Katetov-Tong interpolation theorem holds, this approach leads to a especially transparent and succinct proof of it. It is also shown that this pointfree extension of Katetov-Tong theorem still covers the localic versions of Urysohn's Lemma and Tietze's Extension Theorem. | URI: | https://hdl.handle.net/10316/4615 | DOI: | 10.1016/j.topol.2004.10.022 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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file83f2213bf61e49249d5cbff37ccf3cec.pdf | 162.53 kB | Adobe PDF | View/Open |
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