序拓扑在全序集上定义的一类拓扑,也称全序拓扑. 为了定义序拓扑, 我们需要全序集的概念,在全序集 中,形如 的集合称为一个正向射线,类似定义负向射线,而以所有射线(包括正向的和负向的)为子基生成的拓扑称为 上的序拓扑. 序拓扑有一组由开区间构成的拓扑基. 序拓扑空间的子空间上具有诱导的序拓扑. 它具有良好的分离性. 序拓扑空间是完全正规豪斯道夫( )空间.
... operator topology 算子拓扑 order topology 序拓扑 piecewise-linear topology 逐段线性拓扑 ...
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讨论了半序集和半序拓扑空间中保序集值算子的最小与最大不动点的存在性。
The existence of the minimal and maximal fixed points for order preserving set-valued operators on semi-ordered sets and semi-ordered topological spaces was analyzed.
只要求第二空间是半序拓扑空间,B(D)是相对紧集,所得结果推广了近期相关结论。
It is only required that the second space is partly ordered topological space and B(D) possess the relatively compactness.
研究了MV代数的区间拓扑和序拓扑及MV代数下的拓扑紧性、连结性、完备性和全序性。
This paper researched the interval topology and order topology of MV algebra as well as the tightness, connectedness, completeness and the total-orderness of MV algebra.
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