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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机译:本文的主要目的是研究在哪种条件下T / sub 1 /晶格上的区间拓扑可能是Hausdorff。作者表明,对于T / sub 1 /格L,L上的区间拓扑不能是Hausdorff,除非在极端情况下L与某些X的幂集同构。同理,对于T / sub 1 / -space(X,/ spl part /(X)),/ spl part /(X)上的间隔拓扑不能是Hausdorff,除非在极端情况下(X. / spl part /(X))是离散的。
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