• Title/Summary/Keyword: ${\sigma}$-coherent frames

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σ-COHERENT FRAMES

  • Lee, Seung On
    • Journal of the Chungcheong Mathematical Society
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    • v.14 no.1
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    • pp.61-71
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    • 2001
  • We introduce a new class of ${\sigma}$-coherent frames and show that HA is a ${\sigma}$-coherent frame if A is a ${\sigma}$-frame. Based on this, it is shown that a frame is ${\sigma}$-coherent iff it is isomorphic to the frame of ${\sigma}$-ideals of a ${\sigma}$-frame. Finally we show that ${\sigma}$-COhFrm and ${\sigma}$Frm are equivalent.

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COUNTABLY APPROXIMATING FRAMES

  • Lee, Seung-On
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.295-308
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    • 2002
  • 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.

Stably 가산 근사 Frames와 Strongly Lindelof Frames

  • 이승온
    • Journal for History of Mathematics
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    • v.16 no.1
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    • pp.63-72
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    • 2003
  • This paper is a sequel to [11]. We introduce $\sigma$-coherent frames, stably countably approximating frames and strongly Lindelof frames, and show that a stably countably approximating frame is a strongly Lindelof frame. We also show that a complete chain in a Lindelof frame if and only if it is a strongly Lindelof frame by using the concept of strong convergence of filters. Finally, using the concepts of super compact frames and filter compact frames, we introduce an example of a strongly Lindelof frame which is not a stably countably approximating frame.

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