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For example, the cofinality of ω is ω, because the sequence ω·''m''( where ''m'' ranges over the natural numbers ) tends to ω; but, more generally, any countable limit ordinal has cofinality ω.

例如，ω的共尾性是ω，因为序列ω·''m''(这里的''m''取值于自然数之上)趋向于ω；但是，更加一般的说，任何可数极限序数都有共尾性ω。

In chapter 5, local derivations and local automorphisms of nest subalgebras in von Neumann algebras and local higher cohomology -local 2-cocycles are studied. It is proved that every weakly continuous local derivation, respectively, every weakly local automorphism, of nest subalgebra of a factor von Neumann algebra is a derivation, respectively, an automorphism. Every norm continuous local derivation, respectively, every norm local automorphism, of the nest subalgebra associated to a countable nest in a factor von Neumann algebra is a derivation, respectively, an automorphism. Moreover, it is answered Larson's question. Finally, it is shown that every local 2-cocycle of any von Neumann algebra is a 2-cocycle.

第五章研究von Neumann代数中套子代数的局部导子和局部同构以及von Neumann代数的高维局部映射—局部2-上循环，证明了因子von Neumann代数中套子代数的每一个局部强连续导子和局部强连续同构分别是导子和同构；可数套所对应的套子代数的每一个有界局部导子和有界局部同构分别是导子和同构；同时，部分回答了Larson所提的问题；最后，得到von Neumann代数的每一个局部2-上循环是2-上循环。

Collective noun: These are generally countable nouns, but even in the singular they refer to groups of people, animals or things, such as family, class, team, government, committee, etc.

集体名词一般是可数名词，但就是单数，也指人，动物或事物的群体 2。

In a compact system, the limit set of a point can b e countable or uncountable .

紧空间上的动力系统中一点 x的极限集可能是可数的也可能是不可数的。

The fifth section is the reseach about countable productive property of I-fuzzy first countability in I-fuzzy topological space.

第五部分是关于I-fuzzy拓扑空间中I-fuzzy第一可数性的可乘性的研究。

A number of properties of countable topological space were given systematically, such as its countability, separability, compactness and connectedness, including their proofs on the basis of the nature of topological space, real number space and corresponding theorems.

摘要在可数补拓扑空间的拓扑性质的研究基础上，系统的给出了可数补拓扑空间的可数性，分离性，紧致性，连通性等性质，并给予证明。

The author uses I-fuzzy quasi-coincident neighborhood system to introduce the concepts of I-fuzzy first countability and I-fuzzy second countability, and proves the degree to second countability in each of I-fuzzy topological space must be less than that to first countability, and gives the equivalent characterations about the continuity of function by convergence of sequences in first countable I-fuzzy topological spaces.

作者利用方进明在[4]中提出的I-fuzzy重域系引入了I-fuzzy拓扑空间的第一可数性和第二可数性的概念，证明了一个I-fuzzy拓扑空间空间是第二可数的I-fuzzy拓扑空间的程度一定小于它是第一可数的I-fuzzy拓扑空间的程度，并且在第一可数的I-fuzzy拓扑空间中对映射的连续性进行了等价刻画。

Thus by countable additivity of

一个这样的可能性是使用

And, like natural numbers , integers is a countable infinite set.

和自然数一样，整数也是一个可数的无限集合。

And, like natural numbers , integers are a countable infinite set.

和自然数一样，整数也是一个可数的无限集合。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。