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Order Topology and Bi-Scott Topology on a Poset 被引量：1

Order Topology and Bi-Scott Topology on a Poset
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摘要 In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posers. In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for some kind of posers.
作者 Bin ZHAO Kai Yun WANG
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第11期2101-2106,共6页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China （Grant Nos. 10871121, 11001158）
关键词 Order-convergence order topology bi-Scott topology doubly continuous poset Order-convergence, order topology, bi-Scott topology, doubly continuous poset
分类号 O153.1 [理学—基础数学] O173.1 [理学—基础数学]
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参考文献14

  • 1Birkhoff, G.: Lattice Theory, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, Providence, RI, 1940.
  • 2Frink, O.: Topology in lattices. Trans. Amer. Math. Soc., 51, 569-582 (1942).
  • 3McShane, E. J.: Order-Preseving Maps and Integration Process, Annals of Mathematics Studies, Vol. 31, Princeton University Press, Princeton, N J, 1953.
  • 4Gierz, G., Lawson, J. D.: Generalized continuous and hypercontinuous lattices. The Rocky Mountain Journal of Mathematics, 11,271-296 (1981).
  • 5Zhao, D. S.: The bi-Scott topology on a lattice. Chinese Annals of Mathematics, Ser. A, 10(2), 187-193 (1989).
  • 6Olej~ek, V.: Order convergence and order topology on a poset. International Journal of Theoretical Physics, 38, 557-561 (1999).
  • 7Mathews, J. C., Anderson, R. F.: A comparsion of two modes of order convergence. Proc. Amer. Math. Soc., 18, 100-104 (1967).
  • 8Zhao, B., Li, J.: O2-convergence in posers. Topology and its Applications, 153, 2971-2975 (2006).
  • 9Zhao, B., Zhou, Y. H.: The category of supercontinuous posers. Journal of Mathematical Analysis and Applications, 320, 632-641 (2006).
  • 10Zhao, B., Zhao, D. S.: Lim-inf-convergence in partially ordered sets. Journal of Mathematical Analysis and Applications, 309, 701-708 (2005).

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Acta Mathematica Sinica,English Series
2011年 第11期

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