Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 16 Sep 2019 00:02:08 GMT2019-09-16T00:02:08Z5021On the uniformization of L-valued frameshttp://hdl.handle.net/10316/13637Title: On the uniformization of L-valued frames
Authors: Gutiérrez-García, J.; Mardones-Pérez, I.; Picado, Jorge; Vicente, M. A. de Prada
Abstract: This note discusses the appropriate way of uniformizing the notion
of an L-valued frame introduced by A. Pultr and S. Rodabaugh in [Lattice-valued
frames, functor categories, and classes of sober spaces, Chapter 6 of Topological
and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in
the Mathematics of Fuzzy Sets, Kluwer, 2003]. It covers the case of a completely
distributive lattice L (which is, in a certain sense, the most general one) and studies
the corresponding category of uniform L-valued frames.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/136372009-01-01T00:00:00ZOn the algebraic representation of semicontinuityhttp://hdl.handle.net/10316/4600Title: On the algebraic representation of semicontinuity
Authors: Gutiérrez García, J.; Picado, Jorge
Abstract: The concepts of upper and lower semicontinuity in pointfree topology were introduced and first studied by Li and Wang [Y.-M. Li, G.-J. Wang, Localic Katetov-Tong insertion theorem and localic Tietze extension theorem, Comment. Math. Univ. Carolin. 38 (1997) 801-814]. However Li and Wang's treatment does not faithfully reflect the original classical notion. In this note, we present algebraic descriptions of upper and lower semicontinuous real functions, in terms of frame homomorphisms, that suggest the right alternative to the definitions of Li and Wang. This fixes the discrepancy between the classical and the pointfree notions and turns out to be the appropriate notion that makes the Katetov-Tong theorem provable in the pointfree context without any restrictions.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/46002007-01-01T00:00:00Z