Adding css elements to javascript?
Changing CSS Values with Javascript
I'm reading Baby Rudin and exercise 28 of chapter 2 reads "Prove that every closed set in a separable metric space is the union of a (possibly empty) perfect set and a set which is at most countable." I don't understand why the set must be closed in order for this to be true.  My proof is as follows, and I don't make any reference to the closedness of the set:  Let $E$ be a set in a separable metric space.  Let $B$ be a countable base of that metric space.  Let $P$ be the set of condensation points of $E$.  I claim that $P$ is perfect and $E-P$ is at most countable.  If $p$ is a limit point of $P$, then every neighborhood of $p$ includes at least one point $q$ of P.  For a neighborhood $N_{p}$ of $p$, choose a neighborhood $N_{q} \subset N_{p}$ of $q$.  Since $q$ is a condensation point of $E$, uncountably many points of $E$ are in $N_{q}$, and thus in $N_{p}$.  So $p\in P$ and $P$ is closed.  If $p \in P$, then $p$ is a condensation point of $E$, so every neighborhood $N_{p}$ of $p$ must include uncountably many points of $E$.  If $p$ is not a limit point of $P$, then there exists a neighborhood $N_{p}$ of $p$ such that $N_p$ includes no condensation points of $E$ except for $p$.  This means that every point $q\in N_{p}-\{p\}$ must have a neighborhood $N_{q}$ that does not have uncountably many points of $E$.  For each $b_{k}\in B \cap \mathscr{P}(N_{p})$, choose such a neighborhood $N_{q_{k}} \supset b_{k}$ of some point $q\in N_{p}-\{p\}$.  Now $\{N_{q_{k}}\}$ covers $N_{p}$, and $\bigcup_{k=1}^{\infty}N_{q_{k}}\supset N_{p}$ has at most countably many points of $E$, for it is a union of countably many sets that have at most countably many points of $E$.  This contradicts the assumption that $p\in P$.  So $P$ is perfect.  Let $S=E-P$. There are no condensation points in $S$.  So there exists an open cover $\{N_s\}$, where each $N_s$ is a neighborhood of $s \in S$ with at most countably many elements of $S$. For each $b_{k}\in B \cap \mathscr{P}(S)$, choose such a neighborhood $N_{s_{k}} \supset b_{k}$ of some point $s\in S$.  Then we have a countable subcover $\{N_{p_{k}}\}$ of $S$. As $N_{p_{k}} \cap S$ is at most countable for all $k$, $S$ must be at most countable.  So what am I doing wrong?  Or is Rudin's assumption of closedness extraneous? How can I count the number of records that have a unique value in a particular field in ROR? Do you "gain" your 1st level? Use ALT to move windows in Windows like in Linux In most Linux window managers, one can use the Alt key while clicking and dragging to rearrange windows. This is one of my favorite features of Linux window managers.  Is there a way to do this in Windows 7? Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc How to delete a file in Windows with a too long filename? My wife has several files and folders that somehow ended up having filenames that have caused them to be undeleteable (can't be deleted) by normal means or via the command line. I believe the filenames are too long due to the depth of the folder structures. Does anyone know of a good utility for cleaning up files like this? I'm using a CTE to convert SSRS stored proc's into BO stored proc's, as apparently I can't use temp tables with Business Objects.  I'm having this query:  ;WITH cte1 AS (      SELECT  cv.issue             , cv.customfield             , CAST(STRINGVALUE AS NUMERIC) AS priority_num       --INTO    #temp_priority_val       FROM    proddb1.customfieldvalue cv WITH (NOLOCK)               INNER JOIN proddb1.customfield e WITH (NOLOCK)                  ON  cv.CUSTOMFIELD = e.id                   AND e.cfname = 'Issue Priority')    ,cte2 AS (      SELECT  a.ISSUE             , f.customvalue priority_num       --INTO    #temp_priority       FROM    cte1 a              INNER JOIN proddb1.customfieldoption f WITH (NOLOCK)                  ON  a.CUSTOMFIELD = f.CUSTOMFIELD                          AND CAST(a.priority_num AS NUMERIC) = f.id)   SELECT * FROM cte2    I keep getting an Error converting data type nvarchar to numeric. error on this execution.  The priority_num column is an nvarchar column that is CAST in the first CTE. When I execute this within the original statement that had the temp tables it works perfectly fine. It must be something with the CTE scope? How do I view or install Ubuntu Touch apps? Lots of people have started developing Ubuntu Touch apps for the Ubuntu App Showdown and just in general, and have published them in the Click App Store.  What is the Click App Store, and how do I install apps published in it? How important are headings in SEO My father in law is travelling to France, for 4 days, (01/07-04/07). Is there a minimum duration for which the travel insurance needed to apply for a Schengen visa must be valid? In other words, can his travel insurance cover just the duration of the trip, or should it last longer? How can I set the processor affinity of a process on Linux? How can I set the processor affinity of a process on Linux? In a bash script sometimes you need the user to wait some seconds for a background process to finish.  I usually use for example:  sleep 10   How can I add a kind of progressbar to the script, so the user knows how long to wait?  I installed the command bar but I don't understand the manual. How to get a DOM Element from a jQuery selector? Why does \noindent have such an effect on \rlap and \llap.? $f$ bounded but $f'$ isn't I have an associative array in the form key =&gt; value where key is a numerical value, however it is not a sequential numerical value. The key is actually an ID number and the value is a count. This is fine for most instances, however I want a function that gets the human-readable name of the array and uses that for the key, without changing the value.  I didn't see a function that does this, but I'm assuming I need to provide the old key and new key (both of which I have) and transform the array. Is there an efficient way of doing this? Show the existence of a certain subgroup of F2 How to remove snap completely without losing the Chromium browser? Sort by author in Alpha bibliography How do I make Windows 10's File Explorer open "This PC" by default? I know how to do that on Windows&nbsp;Vista and Windows&nbsp;7, and I know how to do that on Windows&nbsp;8 and Windows&nbsp;8.1, but neither of the ways work with Windows&nbsp;10; it always defaults into the "Home" view.  (I am basically reposting  for Windows&nbsp;10.)