$C$- and $C^{\ast}$-quotients in pointfree topology
Volume 412 / 2002
Dissertationes Mathematicae 412 (2002), 1-62
MSC: Primary 06D22, 06F25; Secondary 54B30, 54G05, 54G10, 18B30.
DOI: 10.4064/dm412-0-1
Abstract
We generalize a major portion of the classical theory of $C$- and $C^{\ast} $-embedded subspaces to pointfree topology, where the corresponding notions are frame $C$- and $C^{\ast}$-quotients. The central results characterize these quotients and generalize Urysohn's Extension Theorem, among others. The proofs require calculations in $CL$, the archimedean $f$-ring of frame maps from the topology of the reals into the frame $L$. We give a number of applications of the central results.
