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Localic real functions: A general setting
Gutiérrez García, Javier; Kubiak, Tomasz; Picado, Jorgehttp://www.sciencedirect.com/science/article/B6V0K-4V5GD2D-1/2/edd60bf3c0415eaa83ce738f97cc0e85
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
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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