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中文摘要：
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T0拓扑总数为4231,拓扑总数为6942.
英文摘要：
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 T0-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.
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