Convert CSV data to Polygons in Mapinfo
Creating polygons from points in Mapinfo
Is "connected, simply connected" Redundant? Here are my definitions of &quot;connected&quot; and &quot;simply connected.&quot;  A topological space $X$ is connected if and only if it is not the union of two nonempty disjoint open sets. A topological space $X$ is simply connected if and only if it is path-connected and has trivial fundamental group (i.e. $\pi_1(X)\simeq\{\mathrm{e}\}$ and $|\pi_0(X)|=1$).  It is a classic and elementary exercise in topology to show that, if a space is path-connected, then it is connected. Thus, if a space is simply connected, then it is connected. Yet, despite this implication, I've read several cases where the words &quot;connected, simply connected&quot; appear together. For example, in Kobayashi and Nomizu's Foundations of Differential Geometry, Volume 1, page 252, the following is written: &quot;Let $M$ be a connected, simply connected analytic manifold with an analytic linear connection.&quot; In  and  (Links to Journal Storage, also known as JSTOR), they use &quot;connected, simply connected&quot; on their first page. The first of these takes it a step further, referring to &quot;closed, compact, connected, simply connected $4$-manifolds,&quot; where a closed manifold (unfortunate terminology) is defined as a compact manifold without boundary. My question is simple: Why use the words &quot;connected, simply connected&quot; when being simply connected implies connectedness? Thank you. How does one [easily] calculate $\sum\limits_{n=1}^\infty\frac{\mathrm{pop}(n)}{n(n+1)}$, where $\mathrm{pop}(n)$ counts the number of bits '1' in the binary representation of $n$? Is there any trick to calculate the sum? From what I already have, it definitely converges. Currently, moderators have the ability to reset a user's username and/or profile text, and propagate that to the rest of the network, resetting it everywhere. However, often, the user's stackexchange.com network profile will also need to be reset, and this is currently only possible to do by either the user in question or staff.  Instead of bothering staff every time, moderators should have something available similar to chat, where moderators can change a user's parent site and have access to a "refresh profile" button, which will fetch updated information such as username and avatar from the parent site.  Currently, the only thing that moderators can do on stackexchange.com is to see hidden accounts. It would make sense for moderators to be able to refresh profiles there, like chat, and avoid pinging CMs every time this comes up. Prove that a function is not injective How to remove/install a package that is not fully installed? How best to determine if an argument is not sent to the JavaScript function I have now seen 2 methods for determining if an argument has been passed to a JavaScript function. I'm wondering if one method is better than the other or if one is just bad to use?   function Test(argument1, argument2) {       if (Test.arguments.length == 1) argument2 = 'blah';        alert(argument2);  }   Test('test');   Or   function Test(argument1, argument2) {       argument2 = argument2 || 'blah';        alert(argument2);  }   Test('test');   As far as I can tell, they both result in the same thing, but I've only used the first one before in production.  Another Option as mentioned by :  function Test(argument1, argument2) {     if(argument2 === null) {         argument2 = 'blah';     }      alert(argument2); }   As per Juan's comment, it would be better to change Tom's suggestion to:  function Test(argument1, argument2) {     if(argument2 === undefined) {         argument2 = 'blah';     }      alert(argument2); } Is it possible to allow usage for an app or program for a specific times on a Mac? I was trying to achieve this using a second account (which is the admin account) and Parental Controls, but it seemed this isn't possible to do so.  I know there are some programs which you can download that help you with this, (Cold Turkey, for example). But, it would be much easier if I could do this using only tools already available on macOS. When there is a Personal Hotspot network available, it displays a chain link icon instead of the usual lock icon in the list of available networks on iOS and OS X.    My question is, how does OS X distinguish these networks? Is it specified in 802.11 how hotspots broadcast their SSID's differently? I've just purchased a new brand laptop with 17 inch size of the screen. I've installed Texmaker and it is messy. The icons are very small and the GUI is not zoomed out automatically to fit the contents of the window. These are pictures         I've already set the size of the icons to medium and the size of apps to 250 (i.e. the recommended size) for  the display.  I'm using Windows 10. Some fonts are blurry and a lot of people are complaining about this problem with no solution from Microsoft. Any suggestions? Is there any way to script Windows 10's "color filter" feature programmatically? Align Caption to the left I don't understand how to use Fermat's little theorem to find remainders e.g if we are asked to find remainder of $50^{50}$ on division by $13$, what is a and what is $p$ in the formula?  Also I wanted to check can we use both congruence classes as well as Fermat's little theorem to find such remainders? How would be write $50^{50}$ on division by $13$ in terms of congruence classes to find the remainder?  I don't exactly understand what a congruence class is, what does it tell us and how is it related to this? One of our websites was copied word for word all 400 pages by someone who used a special program to clone the site. We saw the program in the code.   This was done in early April and soon after that we lost a lot of rank in Google. We just discovered the copied site today. It is mirrorred 100%.   We did change the front page of our site since then to make some differences but since the Penguin update, we still have not recovered. We have also corrected the problems in Webmaster Tools. Will the mirrored site affect our Google rank to a severe degree or are there other issues that are affecting us? What can be done about that mirrored site? I would like to know how potential difference is created between two points?Is potential difference created by adding more electrons at one side?If that's the case how to add more electrons at one side?  I'm really looking to know what really constitutes potential difference? better Curve/Text to Mesh generation? The triangulation process of Text to Mesh or Curve to Mesh generates some nasty topology.   I get why, but maybe it could be done a bit nicer? Since text is flat, have ngons instead of hundreds of triangles you'll need to modify anyway?  Another issue is when you then want to use the text as a Volume for particles, which for some reason behave weird when you have unusual topology even though they should be using the volume, not vertex or face positions. "Most importantly" or "more importantly"? Which of the following two sentences is more correct?   "A picture says a thousand words, more importantly in a fraction of a second"    OR   "A picture says a thousand words, most importantly in a fraction of a second"   Nothing important, just my own quotes! Do also suggest, if I can put it in a better way to express what I want to. Proof that if $s_n \leq t_n$ for $n \geq N$, then $\liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n$ This is half of Theorem 3.19 from Baby Rudin. Rudin claims the proof is trivial. What I've come up with so far doesn't seem trivial, however, and is probably also wrong (my problem with it is pointed out below). This makes me wonder whether I'm overlooking some useful fact and/or using an unprofitable approach.  Theorem. If $s_n \leq t_n$ for $n \geq N$, where $N$ is fixed, then  $$ \liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n. $$  Proof. Suppose that $s_n \leq t_n$ if $n \geq N$, but that  $$ \liminf_{n \rightarrow \infty} s_n &gt; \liminf_{n \rightarrow \infty} t_n. $$  Let $E_s$ denote the set of all subsequential limits of $\{s_n\}$, and let $E_t$ denote the set of all subsequential limits of $\{t_n\}$. Then  $$ \inf E_s &gt; \inf E_t. $$  This implies that there exists some $x \in E_t$ such that $\inf E_s &gt; x &gt; \inf E_t$, since otherwise $\inf E_t$ would not be the greatest lower bound of $E_t$. Hence some subsequence of $\{t_n\}$, say $\{t_{n_i}\}$, converges to $x &lt; \inf E_s$.  Lemma. (from Rudin) If $x &lt; \liminf_{n \rightarrow \infty} s_n$, then there exists an integer $N$ such that if $n \geq N$, then $s_n &gt; x$.   By the lemma, there exists an integer $N_0$ such that if $n \geq N_0$, then $s_n &gt; x$.   Now, let $\epsilon = \inf_{n \geq N_0} \{s_n - x\}$. This is where I think my proof breaks down. Can't $\epsilon$ be zero? Then, since $\{t_{n_i}\}$ converges to $x$, there exists an integer $N_1$ such that if $n_i \geq N_1$, then $|t_{n_i} - x| &lt; \epsilon$. But this means that, if $n_i \geq \max\{N, N_0, N_1\}$, we have both  $$ s_{n_i} &gt; t_{n_i}, $$  as well as $s_{n_i} \geq t_{n_i}$, a contradiction. $\mathbb{R}$ with the lower limit topology is not second-countable I am trying to prove that $\mathbb{R}$ with the lower limit topology is not second-countable.  To do this, I'm trying to form an uncountable union $A$ of disjoint, half-open intervals of the form $[a, b)$, $a &lt; b$. Is this possible? I think this would imply the $A$ is open but no countable union of basis elements could coincide with $A$ therefore making the real numbers with the lower limit topology not second-countable.  I think there must exist something like $A$ described above but I am having trouble visualizing it and coming up with a formula to represent it.  Maybe there is some other way to show it is not second-countable. SVD: How to find the columnvector of U corresponding to a singular value equal to zero Could there be an eighth Horcrux?