I'm studying engineering and I'm very interested in knowing more about topology. I've studied Calculus, so I'm not new to the subject. I was looking for a book that's not too difficult, and gives an overview of topology. That way I can know if I'd like to read more about it. What should I read? Edit: do you think that I should study abstract algebra before topology?
I am a graduate student of math right now but I was not able to get a topology subject in my undergrad... I just would like to know if you guys know the best one..
Cannot install vim Positive operator has a positive spectrum? Let $T : \operatorname{dom}(T) \rightarrow H $ be a positive self-adjoint operator, is it then true that $\sigma(T) \subset [0,\infty)$? This is something that sounds natural and I guess that it is true. For bounded operator, this can be easily shown, but the only proof I know cannot be adapted to unbounded operator, so I was wondering if anybody here knows how to show this? What is a word for someone who is experienced and wise, but who deliberately acts naïve?    I don’t intend it for sarcastic use; I’m trying to describe someone succeeding in making people think that that person truly is naïve.   Is there a word for this? Can an abstract class have a constructor? Can an abstract class have a constructor?  If so, how can it be used and for what purposes? SBS 2011 - Is Store.exe High Memory Usage Normal? Web applications that want to force a resource to be downloaded rather than directly rendered in a Web browser issue a Content-Disposition header in the HTTP response of the form:  Content-Disposition: attachment; filename=FILENAME  The filename parameter can be used to suggest a name for the file into which the resource is downloaded by the browser.  (Content-Disposition), however, states in  (The Filename Parameter) that the file name can only use US-ASCII characters:     Current [RFC 2045] grammar restricts   parameter values (and hence   Content-Disposition filenames) to   US-ASCII.  We recognize the great   desirability of allowing arbitrary   character sets in filenames, but it is   beyond the scope of this document to   define the necessary mechanisms.   There is empirical evidence, nevertheless, that most popular Web browsers today seem to permit non-US-ASCII characters yet (for the lack of a standard) disagree on the encoding scheme and character set specification of the file name. Question is then, what are the various schemes and encodings employed by the popular browsers if the file name “naïvefile” (without quotes and where the third letter is U+00EF) needed to be encoded into the Content-Disposition header?  For the purpose of this question, popular browsers being:   Firefox  Internet Explorer  Safari Google Chrome  Opera I'm looking for a paper that could help in giving a guideline on how to choose the hyperparameters of a deep architecture, like stacked auto-encoders or deep believe networks. There are a lot of hyperparameters and I'm very confused on how to choose them. Also using cross-validation is not an option since training really takes a lot of time! Formula for calculating $\sum_{n=0}^{m}nr^n$ I want to know the general formula for $\sum_{n=0}^{m}nr^n$ for some constant r and how it is derived.  For example, when r = 2, the formula is given by: $\sum_{n=0}^{m}n2^n = 2(m2^m - 2^m +1)$ according to   Thanks! Proof that there are infinitely many prime numbers starting with a given digit string To prove the following fact: given any sequence of digits in any base, eg 314159265358979323 base 10, there are infinitely many primes that start with these digits,eg when expressed in decimal they start with 314159265358979323. I think using a prime number theorem will be helpful . But I am still not getting a point of how to start the proof. After hours of banging my brain against my skull, I narrowed down an issue I'm having to the fact that \makeatletter doesn't work inside \newcommand. Commands that I call after \makeatletter are registered as undefined, as if \makeatletter didn't do anything.  Why is this the case?  In the example below, I define two commands. Calling one of them from the document body causes the undefined error, while the other doesn't.  \documentclass[11pt]{book} \usepackage{kvsetkeys}  \newcommand{\commandThatFails}{     \makeatletter \comma@parse{}{} \makeatother }  \makeatletter     \newcommand{\commandThatWorks}{         \comma@parse{}{}     } \makeatother  \begin{document}  Hi there.  \commandThatFails \commandThatWorks  \end{document} What is the volatile keyword useful for? At work today, I came across the volatile keyword in Java. Not being very familiar with it, I found . Given the detail in which that article explains the keyword in question, do you ever use it or could you ever see a case in which you could use this keyword in the correct manner? Why does cycle rendering only use one core from an AMD GPU? Just curious as to how to obtain item drops from the last update.  To clarify, item drops as in weapon skins, crates, anything else Valve added without letting us know, etc.  It seems that after playing a bit, I've gotten no drops, but I've seen players who've gotten drops after a few short minutes of gameplay, but I've been playing for hours.  Is the item drop system like TF2, where you can just idle, get an item drop, come back? Is it like Dota2, where you have to be in the matchmaking system and complete matches for the chance to get drops? Or do you have to be MvP to get item drops? Is it a certain time you play the game?   Also, are weapon and crate drops independent or dependent on each other? Meaning, is the drop counter shared between Weapons and Crates, or are they both separate drop counters? What are drawbacks or disadvantages of singleton pattern? The  is a fully paid up member of the 's , but it lately seems rather orphaned by the developer world. I still use quite a lot of singletons, especially for , and while you have to be a bit careful about multithreading issues (like any class actually), I fail to see why they are so awful.  Stack Overflow especially seems to assume that everyone agrees that Singletons are evil. Why?  Please support your answers with "facts, references, or specific expertise" When to use icons vs. icons with text vs. just text links? where does lspci gather its information from? In  I found "[The   latest   version    of   this   document   ". There I says: "… lspci is a synonym for cat /proc/pci".  Which isn't the case here, on a Crunchbang 10 system (Debian based). No such directory. I do get the basic idea and, as far as I  know, the content of proc is (mainly) created during runtime. (Wrong?). This made me curious:  Question: Where does lspci gather it's information from? And where is this documented? (Where did I miss something?)  &nbsp; Another difference I found: In kernel.org's documentation, under "Table 1-5: Kernel info in /proc"      pci &nbsp;&nbsp;&nbsp; Deprecated info of PCI bus (new way -> /proc/bus/pci/, decoupled by `lspci) Why does Quantum Field Theory use usually Lagrangians rather than Hamiltonains?  I heard many reasons, but I'm not sure which is true.   Some say it's just a matter of beauty, so Lagrangians are more beautiful because they don't break/separate the space-time variables (so space-time is a single variable, like in the Klein-Gordon Lagrangian and Hamiltonian).  Some say that Hamiltonians are not always Lorentz invariant.  Could someone explain in a little bit more details? Chat messages should use consistent icon in iOS app It'd be nice if the chat notifications in the feed used the default Stack Exchange icon like the ones in the inbox do*:     Since items in the feed are grouped so that multiple items from the same site , the site icon helps delimit grouped items a bit less subtlely than the grey divider lines, and chat replies' lack of one causes them to sort of blend in to the previous group.  *Ideally it'd use the icon of the site the room was associated with, but I don't think that information is readily available When I create language plperl , I get error: ERROR:  could not load library "C:/Program Files/PostgreSQL/9.1/lib/plperl.dll": The specified module could not be found.  But in my computer,  "plperl.dll" file is exist in "C:/Program Files/PostgreSQL/9.1/lib/..." folder   ( I can not post illustrative image, this forum require >= 10 reputations)  And if I select * pg_pltemplate, I get:  -[ RECORD 4 ]-+------------------------- tmplname      | plperl tmpltrusted   | t tmpldbacreate | t tmplhandler   | plperl_call_handler tmplinline    | plperl_inline_handler tmplvalidator | plperl_validator tmpllibrary   | $libdir/plperl Cyberpunk/Post-Apocalyptic Sci-Fi series from the 90s or 00s based in Manhattan