T/下标1/-格上的区间拓扑

Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium Pub Date : 1996-12-11 DOI:10.1109/AFSS.1996.583679

Xu Xiaoquan, Liu Yingming

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引用次数: 0

摘要

本文的主要目的是研究在什么条件下T/sub 1/-格上的区间拓扑是Hausdorff的。证明了对于T/下标1/-格L, L上的区间拓扑不可能是Hausdorff，除非在极端情况下L同构于某个集合X的幂集。同样，对于T/下标1/-空间(X， /spl部分/(X))， /spl部分/(X)上的区间拓扑不可能是Hausdorff，除非在极端情况下(X /spl部分/(X))是离散的。

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The interval topology on T/sub 1/-lattices

The main purpose of the paper is to study under which conditions the interval topology on a T/sub 1/-lattice may be Hausdorff. The authors show that for a T/sub 1/-lattice L, the interval topology on L cannot be Hausdorff except in the extreme case that L is isomorphic to the power set of some set X. Similarly, for a T/sub 1/-space (X, /spl part/(X)), the interval topology on /spl part/(X) cannot be Hausdorff except in the extreme case that (X. /spl part/(X)) is discrete.

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Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium

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