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second-countable
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  第二可数
     In this paper, three inequalities about weight, character and density between induced space and its underlying space are discribed, by a lever characterization of interior operators in induced spaces. Based on these results, we prove that induced space is second-countable (first-countable, separatable respectively) if and only if its underlying space is second-countable (first-countable , separatable respectively) for an important type of fuzzy lattices (i. e. co-generated fuzzy lattices).
     利用格值诱导空间中内部算子的层次刻划,得出了格值诱导空间与其底空间之间权、特征及稠密度的三组不等式,从而对一类较广泛的Fuzzy格(即ω-生成的Fuzzy格),证明了诱导空间是第二可数(第一可数、可分)空间,当且仅当底空间是第二可数(第一可数、可分)空间.
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  相似匹配句对
     The second;
     第二,专业设置随波逐流;
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     Second,
     二是对于?
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     The second is B-spline.
     第二种采用B样条函数法;
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     E-government's Second Spring
     电子政务第二春
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     On Countable spaces
     关于可数空间
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  second-countable
We also generalize results of Meyer and Clifton-Kent by showing that, under very weak assumptions, any second-countable topological test space contains a dense semi-classical test space.
      


In this paper, the conception of deviation is set up. With the conception, we have proued a seri s of simple and intersting theorems about limit and continuity and integrability of mapping For example, we have proofed: If X is a second countable and T1-space,(Y,ρ) is a metric space, f: x→Y is a mapping then the set consist of points at which the limit of f(x) exists but doesn't continue is countable set.

本文建立了偏离幅度的概念;利用这个概念,我们证明了一系列关于映射的极限存在与连续性及可积性的简单有趣的定理;例如,我们证明了:设X是第二可数的T_1空间,(Y,ρ)是度量空间,f:X→Y是映射,则f(x)的极限存在但不连续的点只有至多可列个。

A perfect axiom system for semi-order space is proposed. With a standard method one can introduce a topology Yr in the abstract metric space (X,r) with values in the above semi-order space. The main results obtained are as follows: (a) The convergence defined in (X,r) is equivalent to that in (X,Yr); (b) (X,Yr) is a T3 space; (c) (X,Yr) is separable if and only if it is second countable, or a Lindeloef space; (d) The compactness in X is equivalent to the sequential compactness in X.

本文给半序空间设置了一套合理的公理系统,对其上取值的抽象度量空间引入拓扑结构。证明了抽象度量空间中点列的收敛性与同一点列在所引入拓扑下的收敛性是一致的,并在隔离性、可分性及紧性方面得到与通常度量空间中相似的结果。

Let S be a locally compact(second countable) Hausdoff semigroup,ξ1,ξ2,ξn,……be independent random elements of S, if S is right (left)simple with a finite number of idempotents then we have.either sup P {ξ1·ξ2…ξn∈kx-1 }→0 x∈ S as n→∞for every compact set k SOr there exists a sequence a1, a2,…an,…of elements such that all productsξk+1·ξk+2·…ξn · an have limiting distribution, as n→∞(k = 0, 1, 2……)This is an extension of Csiszar's result on a locally compact group([1]).

当S为第二可数局部紧Hausdorff拓扑群时,Csiszar在[1]中给出了S上正则概率测度卷积序列Shift收敛性的一个判据,不少作者曾致力于这一结果在拓扑结构上的改进,本文则是在代数结构上推广了Csiszar的这一结果。

 
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