Applied Categorical Structures

, Volume 19, Issue 2, pp 469-487

First online:

Insertion of Continuous Real Functions on Spaces, Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root

  • Maria João FerreiraAffiliated withCMUC, Department of Mathematics, University of Coimbra
  • , Javier Gutiérrez GarcíaAffiliated withDepartamento de Matemáticas-Matematika Saila, Universidad del País Vasco-Euskal Herriko Unibertsitatea
  • , Jorge PicadoAffiliated withCMUC, Department of Mathematics, University of Coimbra Email author 

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We 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.


Frame Locale Localic real function Insertion theorem Biframe Normal biframe Extremally disconnected biframe Bitopological space Ordered topological space

Mathematics Subject Classifications (2000)

06D22 26A15 54C30 54D15 54E55 54F05