Every closed subset of a Banach separable space is separable
Prove that a subset of a separable set is itself separable
Script for modifying file content in specified files I tried searching previous questions but none worked, or I couldn't adapt them to my needs.  I want to write a script that asks for:   folder criteria old string new string   And replace every file in the specified folder and subfolders (and force user to type one) with specific criteria (for example, it must be a ".cue" file), and:   If the file is read-only, disable it. Search for specified old string in the file content and replace it with new string , and save changes in same file. If the file was read-only, enable it again.   I have this code so far, but I don't know what to do in the do part:  @echo off   setLocal enableDELAYedexpansion  :START set "var2=" set /P var2="type folder "  if "%var2%"=="" goto ERROR  set /p old="old string ? " set /p new="new string ? " set /p files="what criteria ? " echo modifying files...  for /r "%var2%" %%v in (%%files) do (  ???  ) pause  goto START  :ERROR echo type something!! goto START How do I deal with a runaway bride? I killed my first wife once I found out there is a mercenary you can marry who gives you up to 300 gold a day (in Whiterun). The only requirement, of course, being that I had to hire her first. So I hired her, and then I popped the question, to which she replied the usual: tell the priest to arrange the wedding.   When we reached Riften I told her to wait, just outside the bee and barb, and arranged the wedding. I went through the process, and the second it finished she left, I followed but as I left she was nowhere to be seen. I have tried going back to my house, the pub where I hired her and that same spot in Riften about 6 times each now, some during the day, some during the night and cannot find her at all.   Now this isn't to much of a problem because I can re-marry...oh wait, to remarry, my spouse has to die, so I can't claim gold off her and can't remarry, and the autosaves have been used up fast travelling to the places I thought she might've been. My last save is something like 6 levels ago, and I don't want to have to load it.   What should I do about this situation? I have a problem with verb structure In this sentence:     Four items are responsible for three-fourths of the overall spending around the world, the most prominent share being that of food.   Why after the comma, the verb "being" is used? Why it does not use "is"? What language should I speak to my daughter? I am a Greek, born, living and working in France, married to an Albanian woman, working all day in English.  I have a 2,5 year old daughter, who lived from:    September 2014 to April 2015 and February 2014 to April 2014   in Albania (11 months, approx. 36% of her lifespan), where people only talked albanian to her.  I speak only French with my child, BUT I only speak Greek with my wife, because she refuses to speak French with me, because she is insecure in French. Yet, my wife speaks Albanian to my child.  These facts lead to the circumstance, that the language development of my child seems a bit delayed, because she doesn't yet make three word sentences.  Though I am a little worried about her language development, I want to know, if there is a problem if I also start speaking English to her on a regular basis, since I heard that children are capable growing up learning different languages.  Is there something like a burnout/depression danger in children? Since I can see it in her eyes that she wants to communicate but is not able to and I can see it bothering her a lot.  Should I cut my communication with my daughter down to only French? Should I cut it down to speaking Greek with her, since this is the language I speak with her mother every day? Or should I just continue mixing everything up? Or can I even start speaking English with her?  I don't want her to struggle to the point of extreme frustration, but if this means that in the end, her language development will catch up to normal kids, I am inclined to let her struggle a bit. So are there any longterm deficits for her, if I introduce English?  Please advice.  George Join table depending on value of column in main table Best font for programming? I want to write a function that takes an array of letters as an argument and a number of those letters to select.   Say you provide an array of 8 letters and want to select 3 letters from that. Then you should get:  8! / ((8 - 3)! * 3!) = 56   Arrays (or words) in return consisting of 3 letters each. How can I pad a value with leading zeros? In my scene I have a camera sitting at the origin. I would like to contraint it so that it always looks at the center of a given object. But the camera should not change its position.  I found some answers using a "TrackTo" or "LockedTrack" constraint but could not manage to make it work.  Could I probably use a Driver for this and if yes, how can I adjust it?  Thanks in advance! says that the number of different monomials of degree $M$ in $N$ variables is $$\frac{(M+N-1)!}{M!(N-1)!}\; .$$ Can anyone explain why this is true? Let $\displaystyle f$ be differentiable, $\displaystyle f(x)=0$ for $|x| \geq 10 $ and $g(x)=\sum_{k \in \mathbb Z}f(x+k).$ Proving that $\sum_{n=0}^\infty \sum_{k=0}^n \frac{(-1)^n}{(k+1)\times (n-k+1)}$ converges Etiquette for username changes I'm thinking of changing my username to my real name. Given that I have a presence on some of the sites here (mostly codegolf), what etiquette should I follow when choosing my new name?  As my username is currently Quincunx, I'm thinking of changing it to MyRealName (formerly Quincunx). Or perhaps MyRealName (né Quincunx). Maybe just MyRealName (Quincunx). If I do use these usernames, will people be able to recognize who I am? Or is there already a standard way to change usernames (such as relying on the profile picture)? What should I focus on when converting photos to black and white? When I look at the black and white photographs from professional photographers, I notice that they have a special look. Not a specific style—obviously each photographer has her own style—but a look which make them different from similar color photos, a special feeling, which makes them shine specifically as black and white and makes color irrelevant.  When I convert my own photos to black and white in Lightroom, they don't have any special look. They just look like any other of my photos, simply converted to black and white. I imagine that there are two reasons for that:   Some scenes are better for black and white. Talented and/or experienced photographers know which scenes would be beautiful in black and white, and shoot specifically those scenes. Moreover, they know how to adapt the scene itself and the lighting to black and white (for instance by not relying on the color contrast itself).  In my case, I don't think much about shooting for black and white. It comes only in post-processing, when I either think that the photo will look great in black and white (and very often, it doesn't), or I find the colors to be poor and turn the photo to black and white (which actually doesn't make the photo any better). Post-processing is much more complex than clicking on black and white button in an app. It involves not only adjusting black and white mix (i.e. raising or lowering the lightness of specific colors), but doing lots of other adjustments.  In my case, I do black and white mix, but other adjustments I do are similar to what I would do for a color photo: actually, I may even do them on a color photo, and only then turn it to black and white.   So, what should I take in account if I want to have decent black and white photographs? Are there specific techniques, tips, tricks or warnings for someone who usually shots in color and wants to start black and white photography?  Let me show some examples. Are those scenes not great for black and white photos in the first place? Or can they be salvaged through proper post-processing?  1.  First, a poorly done photo from Scotland with dubious composition and very poor colors that I was unable to correct in Lightroom.  The same image in black and white isn't much better. The difference between the trees and the grass on the hill is barely visible. Houses on the hill fade with the sky much more than in the original version.      2.  Here's a photo of a cute pet.  In black and white, the gap between the mouse's ear and the background is barely visible. There is absolutely no benefit compared to the original.      3.  Finally, an example of a much more contrasty picture. The black and white version is weird, since the lack of color makes it difficult to understand whether the soil is the actual sand or something else. I find the sky to be weird as well, and making the blue channel darker or lighter in Lightroom haven't changed that. How to use San Francisco font on Windows? How to calculate number of days between two given dates? Easy way to earn money on Pokemon Omega Ruby/Alpha Sapphire? I've recently been attempting to complete the Hoenn pokedex. I need a lot of pokéballs and ultra balls to catch em' all. If anyone knows an easy way to do this please simply explain it. I believe that repeatedly challenging the Elite Four may work, but I don't really want to do that. Why do video cables (DVI, VGA) still screw in? I guess I could imagine that there was a time when accidentally disconnecting the monitor would have been catastrophic, though I don't see that being the case today.  Is it just a legacy holdover that they are still secured with screws?  Also, why is it that the video connection is really the only one that is still secured this way?  It seems like the power cable would be a better candidate to be secured with screws.  That really could be catastrophic.  In the end, the reason this question occurred to me is that I've never had a video cable come out when not screwed in, so why the significant security? Combining two sorted lists in Python I have two lists of objects. Each list is already sorted by a property of the object that is of the datetime type. I would like to combine the two lists into one sorted list. Is the best way just to do a sort or is there a smarter way to do this in Python? How to show that topological groups are automatically Hausdorff? On page 146, James Munkres' textbook Topology(2ed),  Show that $G$ (a topological group) is Hausdorff. In fact, show that if $x \neq y$, there is a neighborhood $V$ of $e$ such that $V \cdot x$ and $V \cdot y$ are disjoint.  Noticeably, the definition of topological group in Munkres's textbook differs from that in .  A topological group $G$ is a group that is also a topological space satisfying the $T_1$ axiom, such that the map of $G \times G$ into $G$ sending $x \times y$ into $x \cdot y$ and the map of $G$ into $G$ sending $x$ into $x^{-1}$, are continuous maps.