Applied Categorical Structures

, Volume 19, Issue 2, pp 469–487 | Cite as

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

  • Maria João Ferreira
  • Javier Gutiérrez García
  • Jorge Picado
Article
  • 66 Downloads

Abstract

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.

Keywords

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 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Maria João Ferreira
    • 1
  • Javier Gutiérrez García
    • 2
  • Jorge Picado
    • 1
  1. 1.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2.Departamento de Matemáticas-Matematika SailaUniversidad del País Vasco-Euskal Herriko UnibertsitateaBilbaoSpain

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