We prove that the crumpled cube is simply-connected and uniformly locally simply-connected.
证明了皱褶立方体的单连通性与一致局部单连通性。
Sufficient conditions for a simply-connected domain of 2-dimensional minimal submanifold immerged in 2 + p-dimensional manifold of quasi-constant curvature to be stable were proved.
证明了拟常曲率流形中二维极小子流形上一个单连通区域为稳定的充分条件。
Simply enter the BIOS setup utility while booting with the disk connected.
当引导连接的磁盘时很简单地进入了BIOS设置程序。
As more users and apps are integrated in the identity network, these benefits extend to other network members simply by virtue of their being connected.
随着越来越多的用户和应用集成到身份网络，这些益处延伸到其他网络成员，仅仅是因为他们连接在这个网络上。
You can quickly experience and evaluate IBM's latest modernization solutions by simply logging in and getting connected to a live environment.
通过简单地登录并连接到一个真实环境中，您可以快速经历并评价IBM的最新更新方案。
The signal of one object simply needs to be connected to the method of another.
只需要将一个对象的信号连接到另一个对象的方法。
A virtual printer is simply a piece of software that ACTS like a printer driver; however, the virtual printer doesn't have to be connected to an actual printer.
虚拟打印机即一种可以充当打印机驱动程序的软件；然而，虚拟打印机不需要被连接到一台真实的打印机中。
Once connected to the update site, you simply choose the features you want to install into your copy of Eclipse and start using them.
连接到更新站点后，选择需要安装到Eclipse副本中的功能，安装好后便可以使用这些功能了。
A lightweight Linux distro is a possibility. For example an OS that simply booted up the computer, connected to the Internet, and then opened Firefox.
一个轻量的Linux发行版是可能的，比如一个负责启动计算机，并连接到互联网打开Firefox的操作系统。
Once you're connected, you can simply choose what features to install into your Eclipse.
连接后，便可以选择将什么特性安装到Eclipse中。
In this example, the surface is not simply connected and any smoothed-out object looks like a torus with at least one hole.
在这个例子里，圈饼表面就是非单连通的，并且这类物体的简化就会像是至少有一个洞的曲面。
In many ways, I simply connected the dots in these different strands of thinking and warnings.
在许多方面，我仅仅只是把许多不同思考和警示的线索联系起来。
OK, so where do we use the assumption of being defined in a simply connected region?
那么我们是在哪里利用了，“定义在单连通区域”的假设呢？
OK, so for this guy, domain of definition, which is plane minus the origin with the origin removed is not simply connected.
好滴，目前这里，在有定义的区域里，减掉原点，即移去原点，就不是单连通的。
And here, to be completely truthful, I have to say defined in a simply connected region. Otherwise, we might have the same kind of strange things happening as before.
这里，为了使得完全成立，不得不假设，这定义在一个单连通区域，否则就有可能得到，和先前一样的奇怪事情。
Or, as we will see soon, in a simply connected region.
稍后我们会知道，在一个单连通区域上也可以。
It seems difficult to explain why Skyscrapers and economic crisis are so closely connected simply by coincidence. So what on earth are the reasons for that?
摩天大楼与经济危机的关联如此密切，很难用巧合来理解，那么究竟是什么原因让经济危机总是与摩天大楼如影随形呢？
A wire is simply a connection in the assembly diagram that indicates which reference is connected to which component.
连线是指组装图中的连接，表示某个引用被连接到某个组件。
Who thinks it's not simply connected?
谁认为它不是单连通的？
Because an element with an output that isn't connected will simply sit there waiting for someone to consume its output.
因为如果元素带有断开的输出，那么它将会等待其他元素消耗其输出。
Who thinks it's simply connected?
谁认为它是单连通的？
Any object with a simply connected surface can be smoothed out to look like a sphere.
任何具有单连通表面的物体都能简化成一个球体。
And, maybe on the final it would be, there won't be any really, really complicated things probably, but you might need to be at least vaguely aware of this issue of things being simply connected.
期末考也可能会用得上，实际上，真的不会有十分复杂的问题，不过你们也要大概地了解一下,这个关于单连通区域的知识点。
Let's not worry too much about it. For accuracy we need our vector field to be defined in a simply connected region.
对于它，不用太担心，为了精确起见，需要向量场定义在一个单连通区域中。
And, that's where the assumption of simply connected is useful.
在这里单连通的假设是有用的。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
OK, so anyway, that's the customary warning about simply connected things.
总之，这是关于单连通的习惯性提醒。
Well, if you know that your vector field is defined everywhere in a simply connected region, then you don't have to worry about this question of, can I apply Green's theorem to the inside?
如果知道了，向量空间在单连通区域内处处有定义，那么就可以毫无顾忌地，在这个区域里使用格林公式了？
His conjecture, made in 1904, was that in this four-dimensional world, all closed three-dimensional surfaces that are simply connected could be transformed to look like a three-dimensional sphere.
他在1904年就提出猜想：在四维空间，所有单连通的封闭三维面都能转化为一个三维球体。
So, that's one way to check just for sure that this thing is not simply connected.
这是检验,该区域不是单连通的一种方法。
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