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COUNTABLY APPROXIMATING FRAMES

  • Published : 2002.04.01

Abstract

Using the Countably way below relation, we show that the category $\sigma$-CFrm of $\sigma$-coherent frames and $\sigma$-coherent homomorphisms is coreflective n the category Frm of frames and frame homomorphisms. Introducting the concept of stably countably approximating frames which are exactly retracts of $\sigma$-coherent frames, it is shown that the category SCAFrm of stably countably approximating frames and $\sigma$-proper frame homomorphisms is coreflective in Frm. Finally we introduce strongly Lindelof 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

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