This semester I have a course on topology. I'd like you to recommend me some books.
Possible Duplicate:           What book would you recommend for an undergraduate wanting to learn the basics of topology? I've come across several books that claim to give an introduction to the subject, but I wasn't sure which one(s) to pick.  Here are some of the books I came across:   Introduction to Topology - Bert Mendelson Basic Topology - M.A. Armstrong First Concepts of Topology - William G. Chinn Topology Without Tears - Sidney A. Morris Topology - James Munkres   They don't go over the exact same topics, some are more in-depth than others, some seem to target slightly different audiences etc. What would be right for me (not necessarily from that list)? To give some more background, I want to learn topology because I feel it will be somewhat helpful in the field of Computer Vision.
Proof or disproof that every integer can be written as the sum of a prime and a square. I'm refreshing some algebra and in the beginning chapters of my book I'm presented with the following simple looking problem that I got stuck on:      Prove or disprove: If $n$ is a positive integer, then $n=p+a^2$, where $a$ is an integer and $p$ is prime or $p=1$.   At first I thought $n=13$ would give a nice counterexample, but then I noticed my book defines primes to include the negative primes. Now $13=-3+4^2$ is a solution.   I am allowed to use the fundamental theorem of arithmetic and the division and euclidean algorithms. I tried to express $n$ and $a$ by their prime factorizations, but I didn't get anywhere from there. I would like a hint which direction to take. Am I just missing something silly? $X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed Let $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$   Show that $X$ is Hausdorff if and only if $D$ is closed in $X \times X$.   First, I tried to show that $X \times X \setminus D$ is open using the fact that $X \times X$ is Hausdorff (because $X$ is Hausdorff), but I couldn't find an open set that contains a point outside $D$ and is disjoint to it... Math.cos() gives wrong result Q&A blank in Stack Exchange Android app v1.0.95 - S10e/Android 10 Recently upgraded to a Samsung S10e and Android 10, but all Q&amp;A in the Stack Exchange app v1.0.95 are blank.  The title and comments are visible, but question/answer posts are just white space. Accessing the About page in the app is also blank.  I tried clearing data, cache and re-installing the app, but I still get the same behaviour. Why do we need Diffie Hellman? Diffie–Hellman offers secure key exchange only if sides are authenticated. For authentication, sides are using public/private key. So if side A knows the public key of the side B, then A can simply use that key to encrypt the message (or the new session key).  Why bother to use separate key exchange algorithm? How to deal with long pre-bled brake line? I know that the emergency services can be called FREE in the UK by dialing 999 and in the US by dialing 911.   What I don't know is the number to call in other countries and if there is a cost involved. This is something I think most people should find out before travelling but many don't (including me). Hopefully this will help me and other people. Combining  with allowframebreaks in beamer "Install Spotify" can't be opened because Apple cannot check it for malicious software I'm running macOS 10.15 Catalina Beta.  When I try to install Spotify I see the following error:    Is this a Spotify issue or a Catalina issue?  Thanks. How to initialize all members of an array to the same value? How do I set access permissions per field? What I need to do  I have some user account fields that should be administrator-only (read/write/edit).  For example, the IP address used to register.  So, I want to restrict access to administrators.  Current state of field permissions in Drupal 8 (as of Feb 19, 2016)   In Drupal 7, I used the  module.  However,  There is a , but this has been going on for seven years and is marked as "postponed." Separate and visually indicate reversed events from the day's reputation changes We've been getting a lot of questions  ever since the feature to see event reversals such as deleted posts and serial voting was added into the reputation history; and their confusion is legitimate. Even well-respected users have become confused by that number above the day. It should display the reputation changes for that day. I propose that reversal events such as these be visually separated from the main events for that day and not included in the total reputation change for that day. After all, their reputation isn't actually changing for that day, but reversing changes from previous days. These events already seem to get bumped down to the bottom of the events for the day, why not add a simple separator between them? Events indicating reversals    Events which have been reversed     Perhaps a second, smaller number could be added next to the main one to indicate that other events took place on that day, but I feel most users who really care will have noticed or went looking for the events anyways. However, including them in the actual change only serves to confuse people. Cannot make a static reference to the non-static method Before 1994 the last Triwizard Tournament had been held in 1792, where the three headmaster judges were injured by a rampaging cockatrice.  The tournament is held every 5 years, which would put the next one in , the year . Did they carry on with the tradition, or was it deemed too risky again? Show some indication that account is banned from asking new questions What does closed form solution usually mean? This is motivated by  and the fact that I have no access to Timothy Chow's paper  indicated there by Qiaochu Yuan.  If an equation $f(x)=0$ has no closed form solution, what does it normally mean? Added: $f$ may depend (and normally does) on parameters.   To me this is equivalent to say that one cannot solve it for $x$ in the sense that there is no elementary expression $g(c_{1},c_{2},\ldots ,c_{p})$ consisting only of a finite number of polynomials, rational functions, roots, exponentials, logarithmic and trigonometric functions, absolute values, integer and fractional parts, such that   $f(g(c_{1},c_{2},\ldots ,c_{p}))=0$. What is this Windows 8 icon for as rectangle icon in the title bar? Every Window in Windows 8 got this icon if it gots the focus. When clicking on it, nothing seems to happen.   How does this icon work? A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$. Which story is true at end of the movie "Life of Pi"? At the end of the movie  Pi tells us two stories. One with the tiger (unrealistic) and one without the tiger (realistic).  I believe that he was metaphorically referring himself as the tiger who enters the forest (world) after being rescued.  Is my thinking correct? can you explain me the ending?  At the end did Irfan Khan (older Pi/narrator) say that "even God chose the first story"? Does it mean that the first story was indeed real? Factoring $x^n + y^n$ over the integers