Let $X \subseteq \mathbb P^n$ denote a projective variety. When $X$ is a Hausdorff space (we're talking about $X$ as about a topological space with Zariski topology)?  Almost never, I believe: only if $X$ is finite.  I need this fact to finish a simple proof but I haven't any ideas on how to prove it.
A topological space $X$ is said to be irreducible if it cannot be written as a union $X = A∪B$, where $A$ and $B$ are proper closed subspaces of $X$  I want to try the following:  Show:  $(i)$ That every set with the indiscrete topology is irreducible, and every infinite set with the finite complement topology is irreducible.  $(ii)$ That an irreducible Hausdorff space contains at most one point.  Can you give me any suggestions on how to try this?
Dependency error while installing WINE Every time I try to install "WINE" VIA the Software Center on Ubuntu 12.10, I get this error:  The following packages have unmet dependencies:  wine1.4: PreDepends: dpkg (&gt;= 1.15.7.2~) but 1.16.7ubuntu6 is to be installed          Depends: libc6 (&gt;= 2.14) but 2.15-0ubuntu20 is to be installed          Depends: wine1.4-amd64 (= 1.4.1-0ubuntu1) but 1.4.1-0ubuntu1 is to be installed          Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not going to be installed   When I try installing it VIA the terminal, this is what I get:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine1.4 : Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not installable            Recommends: gnome-exe-thumbnailer but it is not going to be installed or                        kde-runtime but it is not going to be installed            Recommends: ttf-droid            Recommends: ttf-mscorefonts-installer but it is not going to be installed            Recommends: ttf-umefont but it is not going to be installed            Recommends: ttf-unfonts-core but it is not going to be installed            Recommends: winbind but it is not going to be installed            Recommends: winetricks but it is not going to be installed E: Unable to correct problems, you have held broken packages.   how do I fix this? In the DC Comics Universe, What Happens to Earthlings Under a Red Sun? I have a windows 7 user who belongs to admin group. I want to execute sc command that requires admin privileges. I DON'T want to open an elevated cmd, want to be able to simply Win+R->Enter command, enter password and that's all. I tried the runas command, but it doesn't seem to work:  &gt;runas /user:me "cmd"   and it asks for a password, and then the command is executed with normal privileges. I know I could use /user:administrator but I don't know the admin pass and I think the admin user (me) should work. Workflow for UV orientation How to I deal with unwrapped UVs orientation?   Delete the default Cube. Add a Cylinder Edit mode and edge select the Top and the Bottom and a single connecting edge. Make them into seams UV Unwrap (standard Unwrap mode)   The unwrapped UV now shows two circles above a row of quads. I can save this and open it in an image editor and paint over those areas and get the texture to align on the cylinder back in blender.  But, the pattern(just happens to be text) that was inserted in place of the row of quads is now upside down on the model. Any attempt to flip or align just makes things worse, from upside down to mirrored or the Top/Bottom not aligning.  So my real question is how could I have known that the quads represented an upside down view of the world?  Do other blender users export UVs and mark them with arrows and colours just to see how they align on a model before actually painting for real?  I tried selecting the edges in step 3 in different orders before making them into seams and it made no difference.  I also looked at the Normals but they appear to be only Inside/Outside not Up/Down.  Blender 2.70 Logical or operator not behaving as expected Like many others, I commonly find myself ending a sentence with a preposition.  Yes, it makes me cringe.  I usually rewrite the sentence, but sometimes (in emails) I just live with it.  To, with... you know who you are.  Should I keep fighting myself on this one, or is it okay in some circumstances? Recovering from forgotten lock pattern My son has an impression tablet 10 and has forgot the lock pattern. How can we reset it without knowing the code? Is $f(x)=10$ a periodic function? I am not getting satisficatory explanation for this. Clearly $f(x+T) = f(x)$ for all values of $T$.  If we assume it is periodic, does this mean period =  $0$? This is maybe a duplicate like , but the error still appears.    When I try to click "mark as duplicate" a HTTP 404 error occur.  I'm using Firefox 16.0.2 with Firebug on Mac OS X 10.5.8 "It is to be discussed", what is the infinitive doing in this sentence? It is to be discussed.   Is be + infinitive forming the future tense here?      You are to be dressed and ready by 8:00.   I was thinking it's almost commanding (or speaking of a command) but this doesn't seem to be the case, as sentences like this are commanding without this structure:     You will be dressed and ready by 8:00.   or      You are going to be dressed and ready by 8:00.   And there's sentences like this that don't imply commandment in any way:     I am to go home tomorrow!   or     I am to be home tomorrow!   (Slightly different meaning, same general sentiment)  So what's going on with the be + infinitive structure? Possible to get type of an aliased type in c#? Type.GetType("System.String")   Is there a lookup for the aliases available somewhere?  Type.GetType("string")   returns null. Strip HTML from Text JavaScript What's a word for someone who is constantly asking for same thing? Where has the trailing newline char gone from my command substitution? I'm in a conversation and I don't really want to leave because the people there keep adding me back so it's just whatever. But I would like to mute the conversation or something like I do on Facebook so I won't take notifications or anything from there unless I press on the group and see what's going on. Because for now I have my Skype having a new notifications every half a second.  Any solutions to that? Reading text file with NSString:stringWithContentsOfFile? Radical change of favourite tags doesn't reflect in questions list How do the tens­es and as­pects in English cor­re­spond tem­po­ral­ly to one an­oth­er? Non-na­tive speak­ers of­ten get con­fused about what the var­i­ous tens­es  and as­pects mean in English. With in­put from some of the folk here I've put to­geth­er a di­a­gram that I hope will pro­vide some clar­i­ty on the mat­ter.  I of­fer it as the first an­swer to this ques­tion. Con­sid­er it a liv­ing doc­u­ment. In­put is wel­come, and good sug­ges­tions will be  in­cor­po­rat­ed in­to the di­a­gram.    No­ta bene: What this is not is a dis­cus­sion of whether there are  more than two tens­es in English. , to which this ques­tion is not in­tend­ed to sup­ply ar­gu­ments one way or the oth­er.  Here, the aim is to pro­vide an overview of what con­struc­tions English-speak­ing peo­ple use for con­vey­ing in­for­ma­tion about ac­tions re­fer­ring to past, present, and fu­ture, and to pro­vide it first and fore­most to pre­cise­ly the peo­ple who are like­ly to use "tense" as a catch-all term in their search, rather than to lin­guists who know bet­ter.  Break­ing News There is now an ex­cel­lent ELU blog ar­ti­cle ti­tled  . It is high­ly rec­om­mend­ed read­ing. How to recover deleted files? Are there any tools, methods, incantations to recover recently deleted files on Ubuntu?  If it makes any difference, I want to recover a  2.x database file. But would be better to have a method/tool that works on any kind of file. Why rationalize the denominator?