Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SPECTRAL DUALITIES OF MV-ALGEBRAS

  • Choe, Tae-Ho (Department of Mathematics & Statistics McMaster University) ;
  • Kim, Eun-Sup (Department of Mathematics College of Natural Sciences Kyungpook National University) ;
  • Park, Young-Soo (Department of Mathematics College of Natural Sciences Kyungpook National University)
  • Published : 2005.11.01
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Abstract

Hong and Nel in [8] obtained a number of spectral dualities between a cartesian closed topological category X and a category of algebras of suitable type in X in accordance with the original formalism of Porst and Wischnewsky[12]. In this paper, there arises a dual adjointness S $\vdash$ C between the category X = Lim of limit spaces and that A of MV-algebras in X. We firstly show that the spectral duality: $S(A)^{op}{\simeq}C(X^{op})$ holds for the dualizing object K = I = [0,1] or K = 2 = {0, 1}. Secondly, we study a duality between the category of Tychonoff spaces and the category of semi-simple MV-algebras. Furthermore, it is shown that for any $X\;\in\;Lim\;(X\;{\neq}\;{\emptyset})\;C(X,\;I)$ is densely embedded into a cube $I^/H/$, where H is a set.

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References

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