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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (4): 457-461    DOI:
    
Finite posets and calculating of the total number of $T_0$-topologies
RONG Yu-yin, XU Luo-shan, XIE Li-na
Department of Mathematics, Yangzhou University, Yangzhou 225002, China
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Abstract  Several important results for finite posets are proved. With these results and the specialization order of a topology, as well as relationships between topologies and orderings, on a 4-element set the total number of $T_0 $-topologies to be 219 and the total number of topologies to be 355 are obtained.

Key words： finite poset      topology      minimal element      the total number of topologies     
Received: 05 May 2015      Published: 19 May 2018
CLC:  0153.1  
  0189.1  
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RONG Yu-yin
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XIE Li-na
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RONG Yu-yin, XU Luo-shan, XIE Li-na. Finite posets and calculating of the total number of $T_0$-topologies. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 457-461.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I4/457


有限偏序集与4元素集合上$T_0$拓扑总数的计算

证明了有限偏序集的几个重要结果, 利用这些结果并借助于拓扑空间对应的特殊化序与拓扑之间的关系计算得出4元素集合上$T_0$拓扑总数为219, 拓扑总数为355.

关键词： 有限偏序集,  拓扑,  极小元,  拓扑总数 
[1] RONG Yu-yin, XU Luo-shan. Rough homeomorphisms and topological homeomorphisms of generalized approximation spaces[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 315-320.
[2] RONG Yu-yin, XU Luo-shan. Calculating of the total number of $T_0$-topologies on a 5-element set[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 461-466.