We generalize a major portion of the classical theory of C- and C*-embedded subspaces to pointfree topology, where the corresponding notions are frame C- and C*-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.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm412-0-1, author = {Richard N. Ball and Joanne Walters-Wayland}, title = {C- and C*-quotients in pointfree topology}, series = {GDML\_Books}, year = {2002}, zbl = {1012.54025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm412-0-1} }
Richard N. Ball; Joanne Walters-Wayland. C- and C*-quotients in pointfree topology. GDML_Books (2002), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm412-0-1/