Lukasiewicz语义集上的紧Hausdorff拓扑

Compact Hausdorff Topology on the Set of Lukasiewicz Semantics

以Ω记从全体命题之集F（S）到单位区间的全体Lukasiewicz赋值之集.本文通过一种自然的方法在Ω上引入了Fuzzy拓扑δ,证明了其为第二可数的零维良紧空间,并证明了δ在Ω上生成的截拓扑空间是第二可数的紧Hausdorff空间,从而是可度量化的空间.

Let Ω be the set of all Lukasiewicz valuations from the set F(S) of all propositions into the unit interval. This paper introduces in a natural way a fuzzy topology δ on Ω, and proves that δ is second countable and zero-dimensional and N-compact. Moreover, it is proved that the cut topology of δ on Ω is second countable, compact, and Hausdorff.