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Examples of topologies in which all open sets are regular? An open subset U of a space X is regular if it equals the interior of its closure, as we learn from the Wikipedia . Furthermore, the regular open subsets of a space (any space) form a complete Boolean algebra.  I'm coming to this from logic and algebra, with not much background in topology. I can't figure out which topologies have "interesting" collections of regular open sets. For example, in the trivial topology and the discrete topology, every open set is regular, if I'm not mistaken. Those are not "interesting" topologies. I assume there are other topologies in which the space X and the null set are the only regular open sets. If so, those aren't "interesting" either, at least not with regard to their regular open ets.  I believe what I'm looking for is topologies in which every open set is regular, other than the ones I've just described.  Thanks for any help. I am using the below script to move two days back when script runs at starting two days of the year and also check first and second days of every month and move two days back. if [$month=&quot;01&quot;] &amp;&amp; [$day=&quot;01&quot;]; then         date=&quot;$last_month/$yes_day/$last_year&quot;         fulldate=&quot;$last_month/$yes_day/$last_year&quot; else         if [$month=&quot;01&quot;] &amp;&amp; [$day=&quot;02&quot;]; then                 date=&quot;$last_month/$yes_day/$last_year&quot;                 fulldate=&quot;$last_month/$yes_day/$last_year&quot;         else                 if [ $day = &quot;01&quot; ]; then                         date=&quot;$last_month/$yes_day/$year&quot;                         fulldate=&quot;$year$last_month$yes_day&quot;                 else                         if [ $day = &quot;02&quot; ]; then                                 date=&quot;$last_month/$yes_day/$year&quot;                                 fulldate=&quot;$year$last_month$yes_day&quot;                         else                                 date=&quot;$month/$yes_day/$year&quot;                                 fulldate=&quot;$year$month$yes_day&quot;                         fi                 fi         fi fi  But my bad am getting the below error message Etime_script.sh: line 19: [06=01]: command not found Etime_script.sh: line 24: [06=01]: command not found What is the correct way to create a single-instance WPF application? What's the Best Way to Shuffle an NSMutableArray? If you have an NSMutableArray, how do you shuffle the elements randomly?  (I have my own answer for this, which is posted below, but I'm new to Cocoa and I'm interested to know if there is a better way.)    Update: As noted by @Mukesh, as of iOS 10+ and macOS 10.12+, there is an -[NSMutableArray shuffledArray] method that can be used to shuffle. See  for details. (But note that this creates a new array, rather than shuffling the elements in place.) Why do corn flakes clump together in milk when stirred? The Cheerios Effect is the name the scientific community has given to this phenomenon. When cornflakes or oats are mixed with milk and stirred, they tend to clump together. Why does this happen? Can physics explain this? Is there a standard naming convention for XML elements? Is there any standard, de facto or otherwise, for XML documents? For example which is the "best" way to write a tag?  &lt;MyTag /&gt; &lt;myTag /&gt; &lt;mytag /&gt; &lt;my-tag /&gt; &lt;my_tag /&gt;   Likewise if I have an enumerated value for an attribute which is better  &lt;myTag attribute="value one"/&gt; &lt;myTag attribute="ValueOne"/&gt; &lt;myTag attribute="value-one"/&gt; Regression - How do I know if my residuals are normally distributed? What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$? For some series, it is easy to say whether it is convergent or not by the "convergence test", e.g., ratio test. However, it is nontrivial to calculate the value of the sum when the series converges. The question is motivated from the simple exercise to determining whether the series $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$ is convergent. One may immediately get that it is convergent by the ratio test. So here is my question:     What's the value of $$\sum_{k=1}^{\infty}\frac{k^2}{k!}?$$ Mean absolute error OR root mean squared error? Why use Root Mean Squared Error (RMSE) instead of Mean Absolute Error (MAE)??    Hi  I've been investigating the error generated in a calculation - I initially calculated the error as a Root Mean Normalised Squared Error.  Looking a little closer, I see the effects of squaring the error gives more weight to larger errors than smaller ones, skewing the error estimate towards the odd outlier. This is quite obvious in retrospect.   So my question - in what instance would the Root Mean Squared Error be a more appropriate measure of error than the Mean Absolute Error? The latter seems more appropriate to me or am I missing something?  To illustrate this I have attached an example below:                    The scatter plot shows two variables with a good correlation,  the two histograms to the right chart the error between Y(observed ) and Y(predicted) using normalised RMSE (top) and MAE (bottom).     There are no significant outliers in this data and MAE gives a lower error than RMSE. Is there any rational, other than MAE being preferable, for using one measure of error over the other? One of the great 'coincidences' in physics is that the Sun happens to shine most brightly at exactly the wavelengths our eyes can see; it's an easy explanation that our eyes evolved to make the most out of what was available.  However, this spectral window is also , with Rayleigh scattering and the ozone layer protecting us from the UV and strong water vapour absorption in the IR until way into the radio range.  My question is: is this a coincidence? Were there geological factors that made it so? Or is it just lucky chance? (I also notice other planets in our neighbourhood weren't quite so lucky.) Or had atmospheric absorption been different our eyes would have tuned to whatever spectral window were brighter as a whole? I have a speed-reading program I purchased with uses dotnet2. However, dotnet2 doesn't run on 64 bit wine. How would I install dotnet2? How are the age restrictions followed by ICC for under 19 cricket tournaments? I have some doubts under this topic,   Can a player aged 19 play under 19 international cricket match? (Since 19 is not under 19) Consider a player having birthday during the series/tournament. How the age will be calculated for him? Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable What can a soldier requisition and for how long? In the military rank feature it says the soldier can "requisition simple equipment or a horse for temporary use". What qualifies as simple equipment, any simple weapon or something less complex than a catapult?  Additionally, which part of the sentence is the "for temporary use referring to, the simple equipment and the horse or just the simple equipment? I've just installed Ubuntu 16.04 LTS on dual boot. I've looked for many solutions and tried them all but Chrome never starts; the logo appears on the left but no window opens.  I downloaded the deb file on google chrome website and installed it through Ubuntu Software, but it doesn't start.   I have tried installing it through the command line with   sudo dpkg -i --force-depends google-chrome-stable_current_amd64.deb sudo apt-get install -f   I have checked with uname -a and my system is 64 bit. I have also tried gdebi with the same result.   My repository universe is up to date.  I only have one display in settings>displays> so I can't turn off built-in display nor check the mirror display (I read it could be the problem as I also have a graphic card but it seems it is not in my case).  Here is what I get in the command line when I try to run Chrome from it ( the message is the same, whatever the method I used to install Chrome):  ~$ google-chrome [11831:11831:1122/114854.195473:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195493:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195508:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195515:ERROR:process_singleton_posix.cc(280)] Failed to create /home/basil/.config/google-chrome/SingletonLock: Permission denied (13) [11831:11831:1122/114854.195538:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195564:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195622:ERROR:chrome_browser_main.cc(1498)] Failed to create a ProcessSingleton for your profile directory. This means that running multiple instances would start multiple browser processes rather than opening a new window in the existing process. Aborting now to avoid profile corruption. [11831:11868:1122/114854.209297:ERROR:browser_gpu_channel_host_factory.cc(108)] Failed to launch GPU process.   Any new approach will be much appreciated How to include a PDF image into a PDFLaTeX document Why is rabies incurable? I'm still not sure about the mechanics that lead to rabies being incurable. I know that it can be treated before any symptoms show up, but why is it that once symptoms show the person is a dead man walking? How do I install a different Python version using apt-get? Probability that $m$ balls will fall into first box Suppose we have $n$ balls that are randomly distributed into $N$ boxes. Find the probability that $m$ balls will fall into the first box. Assume that all $N^m$ arrangements are equally likely.  Attempt: First, we notice that for the first box, we have $n$ choices, and for the second box we also have $n$ choices, and so on. Thus, we have $n^N$ ways to place the balls into the boxes. Pick $m$ balls out of the total $n$ balls, that gives ${n \choose m}$. In how many ways can these $m$ balls go into the first box? Well, in just ${1 \choose 1 }= 1 $ ways. Thus, $$ P = \frac{ {n \choose m } }{n^N } $$ Is this correct? How do I loop through or enumerate a JavaScript object?