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

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.