1) Cauchy sequence
Cauchy序列
1.
The property of a class of special distance space called super-distance space is studied,including its spherical neighbourhood,cauchy sequence,connectedness,completedness, etc.
研究了一类被称为超距空间的特殊度量空间的性质 ,包括它的球形邻域、cauchy序列、连通性、完备性等性质 。
2) Cauchy sequence
Cauchy列
1.
In the given metric space,by using two fixed point lemmas on nonlinear operators,based on track continuous mapping and full-track mapping,the proofs of two theorems which deal with Cauchy sequence convergence to nonlinear fixed point,was given.
在(M,d)度量空间中,通过对两个非线性不动点引理的运用,在轨迹连续映射和完全轨迹型映射下,给出Cauchy列收敛于不动点的两个定理证明,其主要结果加深了对不动点理论的深入研究。
2.
Main results are:① every implication open(closed)ball with radius not less then the norm of the heart point is an MP-filter;② every convergent sequence has unique limit;③ every convergent sequence is a Cauchy sequence;④ if a Cauchy sequence {xn} has a subsequence which converges to a point x,then {xn} converges to x too.
证明了:①每一半径不小于球心范数的蕴涵开(闭)球都是MP滤子;②每个收敛序列都有唯一的极限;③每个收敛序列都是Cauchy列;④如果一个Cauchy列{xn}的某个子列收敛于点x,则该Cauchy列本身也收敛于点x。
3) Cauchy sequence of number
Cauchy数列
4) locally Cauchy sequence
局部Cauchy列
1.
The sequence(x n) in lcs(locally convex separated space)(X,T) is locally Cauchy sequence if and only if there is an increasing unbounded sequence of positive real numbers(a n) such that min{a n,am}(xn? xm)??T→0(m,n→∞).
局部凸分离空间(X,T)中序列(xn)是局部Cauchy列当且仅当存在单调增且趋于正无穷大的正实数列(an),使得min{an,am}(xn-xm)?T?→0(m,n→∞),并得到了一些相关的结论。
5) extensive Cauchy sequence
可拓Cauchy列
6) Cauchy's double alternant
Cauchy行列式
补充资料：Cauchy序列
Cauchy序列
Cauc勿序列!(、u山yseque。。;R加.~~卜“。cl‘] 同基本序列(fondamental sequen优)·
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