If $F\subseteq L\subseteq K$ are fields with $K/L$ and $L/F$ Galois, then $K/F$ is Galois?.
Is normal extension of normal extension always normal?
I am trying to find examples of maps between topological space which are local homeomorphism but not covering maps. Especially, how twisted has to be such a counterexample : can it be a local diffeomorphism between connected manifolds which is not a covering map ?   I found here() a nice proposition which state that a local homeo from a compact space to a connected Hausdorff space is a covering map.   I am interested in all type of counterexamples, from non-Hausdorff spaces to surfaces, to get a better picture of the differences between covering maps and local homeomorphisms.  Thank you ! How come gas molecules don't settle down? If the earth's gravity exerts a net downward gravitational force on all air molecules, how come the molecules don't eventually lose their momentum and all settle down? How is the atmosphere is still miles thick after billions of years? Let$\ p_n$ be the$\ n$-th prime. Can you give me a proof for$\ \prod_{i=1}^\infty \frac{p_i-1}{p_i}=P\approx \frac{1}{11.0453}$? I found$\ \prod_{i=1}^\infty \frac{p_i}{p_i-1}\approx 11.0453$ on . Moreover, writing a paper, should one provide a proof or it is trivial? Thanks in advance. How do I enable Cortana after the Anniversary Update (1607)? What is the reasoning behind limiting "recidivists" to post one question per week? currently restricts recreated accounts to "posting only one question per week..."  I would like to understand why this rate was picked, and not, say, once a day or once a month?  The reason why I ask is that some users limited or banned at Stack Overflow . I expect that learning more about the limitation would help me better understand its impact on Programmers. Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix Mirrored object not symmetrical I am trying to mirror an object and the original is symmetrical along all axis, but when I attempt to mirror across the y axis, the mirrored side is tilted to a different angle. Why do many anime not follow the manga? Why are they usually made shorter? Many anime do not follow the manga history and are made shorter. However there are a few that do follow it or try to finish the history with the manga like the big three (Naruto, Bleach, One Piece), Death Note, and FMA Brotherhood. But others finish the anime without the real ending like FMA, Ouran High School, Pandora Hearts, Tsubasa Reservoir Chronicle. Why is this so? Is it because of the high cost? Or the lack of popularity? Which predictions of The Last Jedi: Darths & Droids Bingo were correct? Combining two covariance matrices I'm calculating the covariance of a distribution in parallel and I need to combine the distributed results into on singular Gaussian. How do I combine the two?  Linearly interpolating between the two almost works, if they are similarly distributed and sized.   provides a forumla at the bottom for combination but it doesn't seem right; two identically distributed distributions should have the same covariance, but the formula at the bottom of the page doubles the covariance.  Is there a way to combine two matrices? Filter dict to contain only certain keys? How to differ sessions in browser-tabs? Can someone tell me what's wrong with this? because i can't figure out where the missing \right( is.  \begin{equation}  \begin{split} Μ=&amp;-\pi \rho \frac{c^{2}}{4}    \left[c\left(\frac{α}{c}-\frac{1}{2}\right)\ddot{h}+Uc\left(\frac{3}{4}-     \frac{α}{c}\right)\dot{\alpha} +\frac{c^{2}}{4}\left(\frac{9}{8}+      \frac{4α^{2}}{c^{2}}-\frac{4α}{c}\right)\ddot{\alpha} \\  &amp;-\left(\frac{4α}{c}-1\right)U C(k) \left(-\dot{h} +U\alpha + c \left(\frac{3}{4}-\frac{α}{c}\right)\dot{\alpha}\right)\right]  \end{split} \end{equation} INC instruction vs ADD 1: Does it matter? Does there exist a function such that $\lim_{x \to a} f(x) = L$ for all $a \in \mathbb R$ but $f(x)$ is never $L$? I've noticed the text of the Hot Meta Posts box is not within its limits. I guess this would happen for any question with a word that's long enough: Create an Application without a Window How would you program a C/C++ application that could run without opening a window or console? Is there a way to show the console in a Windows application?  I want to do something like this:  static class Program {     [STAThread]     static void Main(string[] args) {         bool consoleMode = Boolean.Parse(args[0]);          if (consoleMode) {             Console.WriteLine("consolemode started");             // ...         } else {             Application.EnableVisualStyles();             Application.SetCompatibleTextRenderingDefault(false);             Application.Run(new Form1());         }     } } If $G$ has no proper subgroup, prove that $G$ is cyclic of order $p$, where $p$ is a prime number.     I know that since $G $is a group with no proper subgroups, $g \in G$ is not just the identity. I don't know where to go from there. International TLD's vs. duplicate content I currently work at a pretty big website that has visitors from around the globe. My job is to help out on the SEO, and one thing we've been discussing lately is the use of international TLD's. The ones we use range between:   (partly) translated websites like .es and .de that serve most of the content in the country's language non-translated (english) websites for non-english languages (due to a lack of translations) like .ro and .cz english websites for english speaking countries with localized TLD's (.co.nz, .co.uk)   On one hand I really have the feeling this is causing a lot of duplicate content, especially for the last two categories of TLD's.   On the other hand though it seems a lot like country-specific TLD's tend to score a lot better in that country's Google. Would it be advisable to keep on using these domains, or should we canonicalize them all to the .com version?