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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (4): 461-466    DOI:
    
Calculating of the total number of $T_0$-topologies on a 5-element set
RONG Yu-yin, XU Luo-shan
Department of Mathematics, Yangzhou University, Yangzhou 225002, China
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Abstract  Based on some results for finite posets and the specialization order of a topology, as well as relationships between topologies and orderings, we calculate the total number of $T_0 $-topologies on a 5-element set, which is 4231. We also calculate the total number of different topologies on a 5-element set, which is 6942.

Key words： finite poset      topology      minimal element      the total number of $T_0 $-topologies     
Received: 30 January 2016      Published: 16 May 2018
CLC:  O153.1  
  O189.1  
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RONG Yu-yin
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RONG Yu-yin, XU Luo-shan. Calculating of the total number of $T_0$-topologies on a 5-element set. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 461-466.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I4/461


5元素集合上$T_0$拓扑总数的计算

利用有限偏序集上的几个重要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5元素集合上$T_0$拓扑总数为4231, 拓扑总数为6942.

关键词： 有限偏序集,  拓扑,  极小元,  $T_0$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.