Encontrados 8 documentos, a visualizar página 1 de 1
Rings of real functions in Pointfree Topology
Gutiérrez García, Javier; Picado, JorgeThis paper deals with the algebra F(L) of real functions of a frame L and its subclasses LSC(L) and USC(L) of, respectively, lower and upper semicontinuous real functions. It is well-known that F(L) is a lattice-ordered ring; this paper presents explicit formulas for its algebraic operations which allow to conclude about their behaviour in LSC(L) and USC(L). As applications, idempotent functions are characteriz...
Localic real functions: A general setting
Gutiérrez García, Javier; Kubiak, Tomasz; Picado, Jorgehttp://www.sciencedirect.com/science/article/B6V0K-4V5GD2D-1/2/edd60bf3c0415eaa83ce738f97cc0e85
Insertion of continuous real functions on spaces, bispaces, ordered spaces and ...
Ferreira, Maria João; Gutiérrez García, Javier; Picado, JorgeWe characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales. ; Centre of Mathematics of the University of Coimbra/FCT...
Monotone insertion and monotone extension of frame homomorphisms
Gutiérrez García, Javier; Kubiak, Tomasz; Picado, JorgeThe purpose of this paper is to introduce monotonization in the setting of pointfree topology. More specifically, monotonically normal locales are characterized in terms of monotone insertion and monotone extensions theorems. ; http://www.sciencedirect.com/science/article/B6V0K-4PT1P7X-1/1/58970e75a046926abdd6e67f8939faea
Uniform-type structures on lattice-valued spaces and frames
Gutiérrez García, Javier; Mardones-Pérez, Iraide; Picado, Jorge; Prada Vicente, María Angeles deBy introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures a significant class o...
Completely normal frames and real-valued functions
Ferreira, Maria João; Gutiérrez García, Javier; Picado, JorgeUp to now point-free insertion results have been obtained only for semicontinuous real functions. Notably, there is now available a setting for dealing with arbitrary, not necessarily (semi-)continuous, point-free real functions, due to Guti errez Garc a, Kubiak and Picado, that gives point-free topology the freedom to deal with general real functions only available before to point-set topology. As a rst exam...
Pointfree forms of Dowker and Michael insertion theorems
Gutiérrez García, Javier; Kubiak, Tomasz; Picado, JorgeIn this paper we prove two strict insertion theorems for frame homomorphisms. When applied to the frame of all open subsets of a topological space they are equivalent to the insertion statements of the classical theorems of Dowker and Michael regarding, respectively, normal countably paracompact spaces and perfectly normal spaces. In addition, a study of perfect normality for frames is made. ; Ministry of Ed...
Lower and upper regularizations of frame semicontinuous real functions
Gutiérrez García, Javier; Kubiak, Tomasz; Picado, JorgeAs discovered recently, Li andWang's 1997 treatment of semicontinuity for frames does not faithfully re ect the classical concept. In this paper we continue our study of semicontinuity in the pointfree setting. We de ne the pointfree concepts of lower and upper regularizations of frame semicontinuous real functions. We present characterizations of extremally disconnected frames in terms of these regularizations...
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