证明了扩张实数空间是实数空间的加两点紧化空间，指出了存在着加更多点的紧化空间。
It proved that extended real topological space is compactification space of real topological space added to two points. It pointed out that there exists compactification space added more points.
“假”数据不能代表真实数据在页面上会占据的空间。
"Fake" data doesn't represent the actual space on the page that would be taken up by realistic data.
模糊变量是描述模糊现象的数学方法，它被定义为一个从可能性空间到实数集的函数。
Fuzzy variables are mathematical descriptions for fuzzy phenomena, and are de-fined as functions from a possibility space to the set of real Numbers.
探讨了实数相空间的非线性映射和保守系统准规则斑图的能量画法。
The paper discusses nonlinear mapping in real number phase space and energy method of sub-rule spot map in conservative system.
而采用双精度实数作为系统初值密钥，其提供的密钥空间巨大。
Due to realizing in double-real precision, the algorithms are provided with big secret key space .
它从实数的特性开始并且继续严格的处理顺序，系列，米制空间和在一个变量的微积分。
It begins with the properties of the real Numbers and continues with a rigorous treatment of sequences, series, metric Spaces, and calculus in one variable.
以这些空间点为初始值，利用无约束优化，得到在一定值范围内的原方程组的全部精确实数解。
By taking these spatial points as initial guess, all exact real solutions within a certain range of variables are found using unrestraint optimization.
研究了超实数域上两种有用的拓扑—Q-拓扑和S-拓扑．证明了以下结果：空间（R，Q）是完全不连通的；
Two kinds of useful topologies, i. e. Q -topology and S -topology on the field of hyperreal numbers are studied. The following results are proved: The space ( tR, Q) is totally disconnected;
该算法在解空间内将实数染色体通过反向变换映射到量子位，采用量子位概率指导的实数交叉与混沌变异相结合的方法对实数染色体进行演化搜索。
In this algorithm, real chromosomes were inversely mapped to Qbits in the solution space. Qbits probability guided real cross and chaos mutation were used to real chromosomes evolution and searching.
引进了两点间的距离，但它不是实数，是B空间中的点。
The distance between two points has been introduced, which is not a real number but only a point in B-spa(?) e.
引进了两点间的距离，但它不是实数，是B空间中的点。
The distance between two points has been introduced, which is not a real number but only a point in B-spa(?) e.
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