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Firstly, we recall some notions and results about space theory, including Hausdorff space, Hausdorff distance between sets , Baires category about sets and convex set. Secondly, the semi-continuity, closure, compactness of set-valued maps are introduced in set-valued analysis. Finally, essential point, essential set and essential component are introduced.

其中,空间理论及凸集的基本知识介绍了Hausdorff空间、集合间的Hausdorff距离、集合的Baire分类、以及凸集等四个方面;集值分析部分主要介绍单值映射的半连续性以及集值映射的半连续性、闭性和紧性;本质点、本质集和本质连通区部分主要介绍了本质点、本质集和本质连通区等有关概念和性质。

A basic fact about sets is that there are two sets only when their memberships differ. The membership of the set of things that are phlogiston is exactly the same as the membership of the set of things that are Devil-dealing Salem witches. In each case, there are none. So in each case the set of instances is the set with no members, the null set.

按集合观,不承认这里有不同的共相,因为基础事实是,两个集合不同当且仅当成员不同,而这两个集合是相同的,因为都是没有成员的集合,即空集。

Crawling on all-fours, I made steadily but slowly toward them; till at last, raising my head to an aperture among the leaves, I could see clear down into a little green dell beside the marsh, and closely set about with trees, where Long John Silver and another of the crew stood face to face in conversation.

太阳直射在他们身上。西尔弗已经把他的帽子扔到了他旁边的地上,他的光滑、白皙的大脸盘正热切地闪着光,对着另一个人的脸,作出一副恳求的表情。

Crawling on all-fours, I made steadily but slowly toward them; till at last, raising my head to an aperture among the leaves, I could see clear down into a little green dell beside the marsh, and closely set about with trees, where Long John Silver and another of the crew stood face to face in conversation.

我四肢着地、缓慢而坚定地向着他们爬去,直到最后,我抬头向叶隙中望去,能够清晰地看到下面沼地旁一小块绿色的谷地;高个子约翰和另一个水手正面对面地站在那里谈话。

Seeckt was appointed Hindenburg's successor as Chief of Staff in summer 1919 and set about the construction of an elite force of 100,000 men - the maximum allowed under the terms of the Versailles treaty.

1919年夏,他作为保罗·冯·兴登堡的继任者成为德军总参谋长,并开始着手建设一支十万人的精锐部队——这是凡尔赛条约规定的最大规模。

Pour ganache over cooled brownies in pan; let set, about 20 minutes.

把巧克力倒在冷却的蛋糕上面;静放20分钟。

He hired Mr Klein, and they set about changing things—initially by taking decision-making away from the patronage-heavy local school boards, and then by decentralising it to accountable principals, and by actively piloting experimental charter schools that could be models for others.

接下来,他聘请克莱因作为政府教育部门主管,随后他们二人开始了改革行动:首先,剥夺各校理事会的决策权,这些理事会内部官官相护,效率低下;其次将权力分配给实行责任制的各校校长;然后积极推行特许学校作为试点,从而为其它学校树立榜样。

Then they set about creating images using color points. Hence, color points have become the basic ingredient of their works. But expressionists prefer to express their passion using color lines, so these lines have become an important part of their paintings.

于是他们就用彩点去构造画面,&彩点&构成了他们作品的基本语言;表现派画家更喜欢用&色线&表现他们狂放的激情,于是色线就成为他们的常用语汇。

When finishing the conquest of the western Xhosas, the Cape colonial state set about the creation of a colonial order on the basis of the white supremacy and turned African natives into free-wage labors.

在对科萨人的殖民征服告一段落后,开普殖民政府着手创建以白人霸权为基础的殖民秩序,将非洲原住居民改造为资本主义经济发展所需的劳动力大军。

One day shortly after my wife and I were married, Balenciaga Envelop Clutch , we set about picking new living-room wallpaper from a book of samples.

婚后不久的一天,我和妻子着手从一本样品手册中挑选起居室的壁纸。

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According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm~150rpm时取得最大值,此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世,形体几无变化。

When I was in school, the rabbi explained everythingin the Bible two different ways.

当我上学的时候,老师解释《圣经》用两种不同的方法。