TY - JOUR ID - 87117 TI - The function ring functors of pointfree topology revisited JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Banaschewski, Bernhard AD - Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada. Y1 - 2019 PY - 2019 VL - 11 IS - Special Issue Dedicated to Prof. George A. Grätzer SP - 19 EP - 32 KW - Completely regular frames KW - zero dimensional frames KW - completely regular $sigma$-frames KW - zero dimensional $sigma$-frames KW - real-valued continuous functions and integer-valued continuous functions on frames DO - 10.29252/cgasa.11.1.19 N2 - This paper establishes two new connections between the familiar function ring functor ${\mathfrak R}$ on the category ${\bf CRFrm}$ of completely regular frames and the category {\bf CR}${\mathbf \sigma}${\bf Frm} of completely regular $\sigma$-frames as well as their counterparts for the analogous functor ${\mathfrak Z}$ on the category {\bf ODFrm} of 0-dimensional frames, given by the integer-valued functions, and for the related functors ${\mathfrak R}^*$ and ${\mathfrak Z}^*$ corresponding to the bounded functions.  Further it is shown that some familiar facts concerning these functors are simple consequences of the present results. UR - https://cgasa.sbu.ac.ir/article_87117.html L1 - https://cgasa.sbu.ac.ir/article_87117_d2e1481a97bb9235d4ea8ec563e32744.pdf ER -