A subset is compact iff it is closed and bounded.   I know $[0,1]$ is closed in $\Bbb R$, and the intersection of two closed sets is closed. I don’t know if $\Bbb Q$ is open or closed in $\Bbb R$ and have seen proofs for both.
Statement: $[a, b] \cap \mathbb{Q}$ in $\mathbb{Q}$ is not compact. Thus the interior of all compact subsets of $\mathbb{Q}$ is $\emptyset$.   I am trying to understand the first sentence. I read that a closed subspace of a compact space is compact, so for example, consider the unit interval $[0, 1]$ which is a compact space. Take a closed subspace $[0, 1] \cap \mathbb{Q}$ of $[0, 1]$. This set is closed since it just consists of all the rational numbers in between $0$ and $1$, including $0$ and $1$. So it is a closed subspace of a compact space. But why isn't this compact?
Easiest way to read from and write to files I am currently in a clan with three members. When we tried to initiate a clan war it said we had insufficient clan requirements. Does anyone know what the full requirements are? Is there a minimum clan member requirement? I have an Android device which is running Android 4.0.3 (or something like that).  My little brother decided to try and guess my lock screen pattern the other day, and ended up locking me out.   I have since been unable to log back in to the tablet using my Google Account details. I provided the correct login details, however it says they are incorrect. Could this be connected to the fact I have no internet connection?  I have no internet connection as the device is WiFi only, and the WiFi is currently turned off. I cannot turn it on, as I am locked out.  How can I log back into my tablet without wiping the user data? I'm using Ubuntu 11.04 and I want to free up some space in my root directory, which is overloaded. I especially want to change the path used for installing applications (they are getting installed directly to the root drive).  Another consideration is that I'm working on a MySQL database server. The server is installed in the root directory itself, so I don't want to  risk losing any data.  Please give me some tips to help sort out this problem. What is dependency injection? There have been several questions already posted with specific questions about , such as when to use it and what frameworks are there for it. However,  What is dependency injection and when/why should or shouldn't it be used? I need to define a new command to create a squiggle arrow with some text on it. Something similar to what \xrightarrow command produces but with wiggly arrows as in \rightsquigarrow. The length of the arrow should automatically be adjusted to fit the text above it and I do not know how to handle this part in TikZ. Any ideas would be much appreciated. How to retain HTML5 Attributes on Markup I have a page with certain html markup and element attributes as shown in the snippit below:  &lt;ul class="accordion" data-accordion=""&gt;  When I edit the page as a user with the WP Administrator Role the &lt;ul&gt; remains intact upon page update. Perfect.  Yet when a user with WP Editor Role edits the page, the ul tag saves as follows:  &lt;ul class="accordion"&gt;  Notice the data-accordion attribute is removed.  How can I get WordPress to retain markup tag attributes for users with the Editor role? Pagination not working with custom loop How can I make up for weak grades while applying for a masters? I feel I've received poor grades in my bachelor's degree in Mechanical Engineering - Second Class Second Division as per UK grading system. Having finished my bachelors in the UK I wish to enroll into a masters program in Systems or Mechanical Engineering in the US. I am currently employed by a logistics company in Dubai.   How can I improve my chances of getting into a grad school in the US with what I consider as poor grades? What other factors can strengthen my application? Do ideal gases at zero Kelvin have potential energy? I'm new with LaTeX and I'm trying to make a table with the elements centered vertically and horizontally. I've searched for this question, it seems like most people were trying to do things a little more complicated than this, resulting in complicated answers I couldn't understand. The table below is already centered horizontally, but the elements are aligned to the top of the cells instead of the center. How do I fix this?      \begin{tabular}{*{5}{|c}|}         \hline         $p$ &amp; $q$ &amp; $p \land q$ &amp; $p \lor q$ &amp; $p \to q$\\         \hline         T &amp; T &amp; T &amp; T &amp; T\\         \hline         T &amp; F &amp; F &amp; T &amp; F\\         \hline         F &amp; T &amp; F &amp; T &amp; T\\         \hline         F &amp; F &amp; F &amp; F &amp; T\\         \hline     \end{tabular} Why do I have the "required reviews completed" status on my submission in Elsevier? I had submitted my paper in an Elsevier journal one year back. Now, status update on the submission tracking says "Required reviews completed." However, for the last two weeks still there is no change in the status.  Should I ask the editor what is going on with my submission? Prove that if $a \mid b$ then $\gcd(a,b) = |a|$ Book series with a double planet system and poisonous bubbles that float around 'Search on Yammer' link in search center refiners I have a heavily branded site I'm working on and can't find where the "Search on Yammer" link is being populated from. It appears within the search refiner/filter web part in the left column but none of the display templates reference this.   I'd like to be able to customize the link, placement on the page, etc. without resorting to jQuery to move elements around the page.     And the markup coming through looks like this. The refiners themselves come through a series of display templates but the Yammer link is nowhere that I can see in any of them.   &lt;div webpartid="f09e98eb-6dc3-4a9b-8dbf-65d0fbc7b7c3" haspers="false" id="WebPartWPQ4" width="100%" class="ms-WPBody " allowdelete="false" style=""&gt;     &lt;div class="ms-ref-ctrl"&gt;         &lt;div class="ms-ref-refiner"&gt;             &lt;div id="Container"&gt;                 &lt;h2 class="ms-displayInline"&gt;                     &lt;a class="ms-ref-name ms-displayInlineBlock ms-srchnav-link-selected ms-link" href="javascript:void(window.open(                     'https://www.yammer.com/search?trk_event=o365_search&amp;amp;search='+                     encodeURIComponent(Srch.ScriptApplicationManager.get_current().queryGroups.                     Default.dataProvider.get_currentQueryState().k),'_blank'));" title="Open a new tab to search for this on Yammer"&gt;Search on Yammer&lt;/a&gt;                 &lt;/h2&gt;             &lt;/div&gt;         &lt;/div&gt;     &lt;/div&gt; &lt;/div&gt; &lt;div componentid="ctl00_SPWebPartManager1_g_f09e98eb_6dc3_4a9b_8dbf_65d0fbc7b7c3_csr" id="ctl00_SPWebPartManager1_g_f09e98eb_6dc3_4a9b_8dbf_65d0fbc7b7c3_csr"&gt;             ... refiners populated through display templates ... &lt;/div&gt; Every $n > 17$ is a non-negative integer combination of $4$ and $7$. Why are lamps and mesh lights not illuminating anything? There are several techniques to do a 3 point lighting system.   How do you properly light a scene while using mesh planes as emission light sources?   I'm following , however despite setting up planes to act a lighting sources, the scene is still very dark.      Actual Blender file here: What is the difference between an indeterminate and variable? From Wikipedia-     In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a placeholder in objects such as polynomials and formal power series.   So, how it is different from variable which is also used as a placeholder? What is the use of the indeterminate? latex gives me the error: Ouch---my internal constants have been clobbered As the title states, compiling with latex produces the error, right away:  Ouch---my internal constants have been clobbered!---case 14   I have no idea what this means... I use TexLive 2012. I updated my texmf.cnf and ran fmtutil-sys and texhash. I guess texhash may have messed it up?  Any ideas?  As requested a minimal working example:  \documentclass{article} \begin{document}     Any tex file. \end{document} Merge two data frames while keeping the original row order