Countably approximating frames
Commun. Korean Math. Soc. 2002 Vol. 17, No. 2, 295-308
Printed June 1, 2002
Seung On Lee
Chungbuk National University
Abstract : Using the countably way below relation, we show that the category {\bf $\sigma$CFrm} of $\sigma$-coherent frames and $\sigma$-coherent homomorphisms is coreflective in the category {\bf Frm} of frames and frame homomorphisms. Introducing the concept of stably countably approximating frames which are exactly retracts of $\sigma$-coherent frames, it is shown that the category {\bf SCAFrm} of stably countably approximating frames and $\sigma$-proper frame homomorphisms is coreflective in {\bf Frm}. Finally we introduce strongly Lindel\"of frames and show that they are precisely lax retracts of $\sigma$-coherent frames.
Keywords : frames, countably approximating frames, $\sigma$-frames, $\sigma$-coherent frames, stably countably approximating frames
MSC numbers : 06A99, 54A99, 54D99
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