A formal definition can be found at page 48 of  "Kolmogorov, A. N., Fomin, S. V. (1970). Introductory Real Analysis, Translated and Edited by Richard A. Silverman"  But where is a separate procedure? I do not see the "separation" procedure in my imagination.  p.s.  In my imagination, I have a bounded table R with too many needles that they enough to very-very near to touch all points in original set R. But it's only my imagination.
In the context of topological spaces, I see the following major countability properties:  A space is:   "separable" iff it has a countable dense subset "second countable" iff if has a countable basis "first countable" iff the neighbourhood system of every point has a countable local basis.   (Definitions taken from Counterexamples in Topology by Steen and Seebach, 2nd ed. 1978 -- there may be differences in wording from other sources.)  The question I have is: "separable" into what, exactly? By which I mean to say: what is the thinking behind calling such a condition "separable"?  It appears not to be related to the concept of "separation axioms", which do immediately and obviously invoke an intuitive notation of separation, neither does it seem to have anything to do with "separated sets".  (Anyone using the spelling "seperable" or "seperated" will be immediately downvoted. :-) )
my email limit is exceeded after sending 10-12 emails..what could be the problem..as i have seen the limit is 1000 emails/day.i am not able to find out what could be the problem..Can some give me some suggestions. As i also know we can send 10 emails in a single transaction.I am sending emails in a batch class.  I am calling this batch class on button click and filling emailList with emailsId's.                      String query='Select id from Lead';//No use of this query                     Batch_send_emails bse=new Batch_send_emails();                     bse.query=query;                                                         bse.resendEmails=emailList;                     database.executebatch(bse);           **Batch Class**           if(!resendEmails.isEmpty())           {               for(String s:resendEmails)                {                   emailsLeads.add(s);                }           }           Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();         mail.setToAddresses(emailsLeads);        // mail.setCcAddresses(ccAddresses);         String subject='GoToMeeting Invitation Details for '+subject;         String body='test';          mail.setHtmlBody(body);          mail.setSubject(subject);         Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });          } Search only for the currently active language Issue with particles in blender donut tutorial I have been recently doing the blender donut tutorial and ran into a problem regarding the sprinkle particles. The particles (hair) keep appearing on the underside of the icing. As seen in the image below, most of the hair particles only come out from the bottom of the icing. I tried to readjust the normals but I realised the normals were already correct. (Blue colour donut in image) Someone suggested following through the weight painting part of the tutorial. However, the sprinkles still remain on the underside of the icing. What is the actual problem and how do I solve this?  Particle settings below  Edit: @moonboots Thanks the hair particle problem has been solved. How do I prevent the submersion of the sprinkle particles? How to list available shells for use by command-line? Does each new Horcrux take half of Voldemort's remaining soul, thus taking a smaller piece each time? When you commit a murder and create a Horcrux, you split your soul. It’s been talked a lot about Voldemort splitting his soul in 7/8 parts. But I think his remaining soul was not 1/7 or 1/8 but far more weaker than that because he did not create all Horcruxes at once.  When he created his first Horcrux, his soul was split into 50-50 (diary). But when the second Horcrux was created, it was created by Voldemort only and the first Horcrux soul should have remained intact. Hence it would have been a 25-25 split of Voldemort's main soul. And so on for every split.  Am I right? What should be done when no more Pokemon can be caught? (when full storage) It seems that I can buy 50 more slots using 200 coins, but what if I keep on getting more and more common Pokemons such as Pidgey or Rattata, then the slots will be full again.  Right now, I am sorting by CP (Combat Power) and then "Transfer" the lowest CP Pokemons to the Professor (to give it away), but wonder what is a good or better way to handle this?  (For example, can I combine several Pidgey into one?) We, as high school students have been taught that-because Bohr's model of an atom assigns specific orbits for electrons-that it is better than Rutherford's model. But what Rutherford failed to explain was why electrons don't emit EM waves &amp; fall into the nucleus. I don't see how the introduction of 'atomic orbitals' overcame this defect. Can't it still radiate EM waves? JSON+Node.js - Unexpected token o Do potion effects affect the ender dragon? I am at the ender dragon and have tons of Potions of instant damage. I never got into range, but do the effects even do anything? "Unable to cast object of type 'System.Byte[]' to type 'System.IConvertible'." error in Photo: why and how do I fix it? Unable to install "quickly" on Ubuntu GNOME 15.10 When running:  sudo apt-get install quickly   To install quickly I get this output:  Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package quickly   Why the error and how can I install it then? Not only in ortho: top, front, back.  Please don't link this answer   I want a background image like this guy has -> I'm currently reading Marcus' "Number Fields," and I'm having difficulty proving the following result:  Corollary 2.2: Let $m$ be a squarefree integer. The set of algebraic integers in the quadratic field $\mathbb{Q}(\sqrt{m})$ is $$ \left\{ a + b \sqrt{m} : a,b \in \mathbb{Z} \right\} $$ if $m \equiv 2,3 \pmod{4}$; and$$ \left\{ \frac{a+b\sqrt{m}}{2} : a,b \in \mathbb{Z} ~,~ a \equiv b \pmod{2} \right\}$$ when $m \equiv 1 \pmod{4}$. $\square$  It is easy enough to see that the claimed sets do, indeed, consist of algebraic integers. The other half of the proof proceeds something like this: suppose that $\alpha = r + s \sqrt{m}$ is an element of $\mathbb{Q}(\sqrt{m})$. Then $\alpha$ is a root of the polynomial $$ x^2 - 2rx + r^2 - s^2m $$ In particular, this means that $\alpha$ is an algebraic integer if and only if both $2r$ and $r^2 - s^2 m$ are integers. At this point, the proof stops, and says that this implies the result. And therein lies the problem: I don't see how to make the connection. I do know, for example, that if one of $r,s$ is an integer, then the other one must be, too, i.e., either both are integers, or both are not. However, I cannot get any further than that. Can anyone give me a gentle nudge in the right direction? Thank you very much! Why does Leia's accent change during A New Hope? Optimum Bone To Water Ratio For Pork and Beef Stocks I am tinkering with my stock recipes.   For pork stock I have been using 8 cups of water over a roasted trotter, a roasted backbone section with about 4 inches of rib attached, and a 1/4 inch slab of roasted pork belly.   For the beef stock I have been using 8 cups of water over an equivalent amount of roasted beef bones (knuckles and backbone/rib).   This gives a very flavorful stock and, for cost reasons, I want to determine how much I can reduce the concentration (by adding more water) without reaching too watery a taste.   Does anybody have any guidance on this topic? What invisible flicker do different types of light bulbs have? What waveform does the light coming off different types of artificial light sources have and (of course) what are the underlying physical reason for them?    I was inspired to ask this question because of several things I have been hearing lately.  Firstly, there was a recent TED talk about how .  Researchers have been working on the problem for a little while now and they've made a fairly impressive product, but it was only recently made possible by the LED technology, which has such a fast response that it can easily compare to the transfer rates of electric information condiuits that we normally use.  My understanding is that incandescent bulbs flicker because they have 60 Hz AC power being pulsed through them.  In fact, I think 60 Hz was chosen in the first place because it was a threshold that was unnoticeable to humans.  Looking at a  demonstrates that it has a very significant lag time responding to both the normal electrical phasor and being turned off.  In other words, it flickers but it doesn't go dark at any point in the AC waveform.  Looking for more information, however, I was a little disappointed, since nothing seemed to give a graph of lumens emitted over time for all different kinds of bulbs.  Of course, there isn't just one relevant time scale.  A light could flicker with 60 Hz and also flicker with 2000 Hz (I just made that up).  I'm interested in the complete picture of what lights exhibit what patterns. Could a website force the browser to go into fullscreen mode? I know Wonder Woman has died in canon before, but in which issue did this happen? A hidden process, what it is? [root@datacenteronline ~]# ssh root@192.168.1.172 Last login: Wed Apr 17 09:55:45 2013 from 192.168.1.187 [root@localhost ~]# ls /proc/ | grep 2266 [root@localhost ~]# cd /proc/2266 [root@localhost 2266]# ls attr             cpuset   limits      net            root       statm autogroup        cwd      loginuid    numa_maps      sched      status auxv             environ  maps        oom_adj        schedstat  syscall cgroup           exe      mem         oom_score      sessionid  task clear_refs       fd       mountinfo   oom_score_adj  smaps      wchan cmdline          fdinfo   mounts      pagemap        stack coredump_filter  io       mountstats  personality    stat [root@localhost 2266]# ls -al /proc/2266 total 0 dr-xr-xr-x   7 apache apache 0 Apr 17 09:45 . dr-xr-xr-x 266 root   root   0 Apr 17 09:11 .. dr-xr-xr-x   2 apache apache 0 Apr 17 09:45 attr -rw-r--r--   1 root   root   0 Apr 17 09:45 autogroup -r--------   1 root   root   0 Apr 17 09:45 auxv -r--r--r--   1 root   root   0 Apr 17 09:45 cgroup --w-------   1 root   root   0 Apr 17 09:45 clear_refs -r--r--r--   1 root   root   0 Apr 17 09:45 cmdline -rw-r--r--   1 root   root   0 Apr 17 09:45 coredump_filter -r--r--r--   1 root   root   0 Apr 17 09:45 cpuset lrwxrwxrwx   1 root   root   0 Apr 17 09:45 cwd -&gt; / -r--------   1 root   root   0 Apr 17 09:45 environ lrwxrwxrwx   1 root   root   0 Apr 17 09:45 exe -&gt; /usr/local/apache2/bin/httpd dr-x------   2 root   root   0 Apr 17 09:45 fd dr-x------   2 root   root   0 Apr 17 09:45 fdinfo -r--------   1 root   root   0 Apr 17 09:45 io -rw-------   1 root   root   0 Apr 17 09:45 limits -rw-r--r--   1 root   root   0 Apr 17 09:45 loginuid -r--r--r--   1 root   root   0 Apr 17 09:45 maps -rw-------   1 root   root   0 Apr 17 09:45 mem -r--r--r--   1 root   root   0 Apr 17 09:45 mountinfo -r--r--r--   1 root   root   0 Apr 17 09:45 mounts -r--------   1 root   root   0 Apr 17 09:45 mountstats dr-xr-xr-x   6 apache apache 0 Apr 17 09:45 net -r--r--r--   1 root   root   0 Apr 17 09:45 numa_maps -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_adj -r--r--r--   1 root   root   0 Apr 17 09:45 oom_score -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_score_adj -r--r--r--   1 root   root   0 Apr 17 09:45 pagemap -r--r--r--   1 root   root   0 Apr 17 09:45 personality lrwxrwxrwx   1 root   root   0 Apr 17 09:45 root -&gt; / -rw-r--r--   1 root   root   0 Apr 17 09:45 sched -r--r--r--   1 root   root   0 Apr 17 09:45 schedstat -r--r--r--   1 root   root   0 Apr 17 09:45 sessionid -r--r--r--   1 root   root   0 Apr 17 09:45 smaps -r--r--r--   1 root   root   0 Apr 17 09:45 stack -r--r--r--   1 root   root   0 Apr 17 09:45 stat -r--r--r--   1 root   root   0 Apr 17 09:45 statm -r--r--r--   1 root   root   0 Apr 17 09:45 status -r--r--r--   1 root   root   0 Apr 17 09:45 syscall dr-xr-xr-x  29 apache apache 0 Apr 17 09:45 task -r--r--r--   1 root   root   0 Apr 17 09:45 wchan   Cound anyone tell me what it is? What is the rough estimate of salary value for a taxpayer to pay AMT? For US federal tax, whether a taxpayer is subject to AMT is determined by a complicated way in Instructions for Form 1040, Line 45, which involves an incomprehensible "worksheet to see if you should fill in form 6251".  By simplification and approximation, is there a rule of thumb for an estimate of a salary value of a taxpayer, so that a salary above the value might cause the taxpayer to pay AMT with a big possibility, and a salary below the value might not with a big possibility?  Why do the following two sources seem to differ greatly in estimates of the boundary salary value:    says that  the possible boundary salary value for a single taxpayer  to pay AMT is $53,900.  says that      Taxpayers with small incomes fall within the AMT exemption limits.   That leaves the upper middle class to face the tax, especially those   with incomes between $200,000 and $500,000    Thanks.