I am using the definition of a $\Delta$-complex as given in Hatcher's book   on pg 103.  Now on pg. 104, just before the section on Simplicial Homology, Hatcher remarks that if $X$ has a $\Delta$-complex structure then $X$ is Hausdorff.  I do not see it at all. Is this easy? Does anybody know of a reference where the general topological details of a $\Delta$-comlpex can be found?  Thanks.
Suppose that $X$ is a topological space equipped with a delta-complex structure. Prove that $X$ is Hausdorff.  I can actually "see" why it should be Hausdorff after the hint from Hatcher asks to "think of a delta-complex X as a quotient space of a collection of disjoint simplices".  I would appreciate if somebody can write out a full formal argument showing this proof. I'm trying to start from the definition of Hausdorff but I don't know how to carry on.
Java Interface Usage Guidelines -- Are getters and setters in an interface bad? How do I quickly rename a MySQL database (change schema name)? The MySQL manual at  covers this.  Usually I just dump the database and reimport it with a new name. This is not an option for very big databases. Apparently RENAME {DATABASE | SCHEMA} db_name TO new_db_name; .  This needs to work with , which stores things very differently than . How do I craft command blocks? I went to my friends house, and he was playing Minecraft on the PC. He showed me a command block, but when I went home and opened Minecraft pocket edition, I went to the crafting table but I could not find any command blocks to craft.  What are command blocks and how do I craft them? What is the name of the package for R? I tried aptitude search r, but (unsurprisingly), there are waaaay too many results to sift through. How can I depict vehicle traffic during daytime in a long exposure without washing out the vehicles? If a user is the type of person to consecutively get downvoted to potential negative reputation, so be it. What's the reasoning to maintain a minimum of one?  One reason that may justify this is of trying to not deter new users from the site who haven't read the FAQ and unknowingly and wrongly ask or answer a question. But most of us acknowledge this and not downvote in such a scenario.  So what's the reasoning behind this lower bound of 1? The Python docs say:     re.MULTILINE: When specified, the pattern character '^' matches at the beginning of the string and at the beginning of each line (immediately following each newline)... By default, '^' matches only at the beginning of the string...   So what's going on when I get the following unexpected result?  &gt;&gt;&gt; import re &gt;&gt;&gt; s = """// The quick brown fox. ... // Jumped over the lazy dog.""" &gt;&gt;&gt; re.sub('^//', '', s, re.MULTILINE) ' The quick brown fox.\n// Jumped over the lazy dog.' JSON+Node.js - Unexpected token o Make account merges propagate to chat Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? So i was reading about  on Wiki and I found a interesting thing written there .    It says that the S. radius of the universe is as big as the size of the universe?   How is this possible?  Since most the universe is empty space shouldn't the S. radius of our universe be significantly smaller then 13.7 light years? My dconf/gsettings installation is broken. How can I fix it without Ubuntu reinstall? I run Ubuntu 12.04.1 LTS x64 in VirtualBox. After one very unfortunate misclick (reset saved state instead of load saved state) I got a very annoying problem.  Almost all applications (unity, synaptic, gedit, etc.) print on start:  Using the 'memory' GSettings backend.  Your settings will not be saved or shared with other applications.   And all GUI settings reset after reboot.   Another symptom:  $ GSETTINGS_BACKEND=dconf dconf-editor (dconf-editor:2353): GLib-GIO-WARNING **: Can't find module 'dconf' specified in GSETTINGS_BACKEND GLib-GIO-Message: Using the 'memory' GSettings backend.  Your settings will not be saved or shared with other applications   But /usr/lib/x86_64-linux-gnu/gio/modules/libdconfsettings.so is present.     What I tried (and it didn't help):   sudo apt-get install -f --reinstall  dconf-tools libdconf0 libdconf-dbus-1-0 dconf-service Build dconf-0.5 from sources and make install it Create empty user profile and start programs there   I have to keep current Ubuntu installation so a complete reinstall is not an option for me.   How can I fix it? I am fascinated by the way the CLR and GC works (I'm working on expanding my knowledge on this by reading CLR via C#, Jon Skeet's books/posts, and more).  Anyway, what is the difference between saying:  MyClass myclass = new MyClass(); myclass = null;   Or, by making MyClass implement IDisposable and a destructor and calling Dispose()?  Also, if I have a code block with a using statement (eg below), if I step through the code and exit the using block, is the object disposed of then or when a garbage collection occurs? What would happen if I call Dispose() in the using block anyay?  using (MyDisposableObj mydispobj = new MyDisposableObj()) {  }   Stream classes (eg BinaryWriter) have a Finalize method? Why would I want to use that? \pdfendlink ended up in different nesting level than \pdfstartlink I've got a Windows 10 Computer (home edition), which has 4GB of Ram and an i5 processor. I need to run an old 32 bit accounting programme. The vendor said it won't release a 64 bit version (although a 64bit version exists, it's missing key features from the older version).  The programme installs fine, but when I click on the programme icon, it says the programme won't work on a 64 bit system.   What options do I have?    I've done a fair bit of research, but it seems to run up dead ends.   1) WoW64     Apparently, this is supposed to let you run 32 bits on 64 bit Windows. However, I am not sure how to install it. I think it's for web servers only. However,  says it can work on Windows 7, but doesn't explain how to set it up (or if it will work on Windows 10).  2) XP mode     A 32bit Windows XP emulator. However, it seems to be for Windows 7 only. Also according to this , you need Windows Professional.   3) Virtual Box Machine    Let's you emulate Windows. Seems overkill for my purposes. Plus I would need to buy a 32 bit Windows license. I think it would run slowly with 4GB of Ram.  4) Partition drive into 32bit and 64 bit versions Apparently, you can use the free tool  to split the drive into two and then install separate 32bit and 64 bit versions.   Again, seems overkill and it looks like I would need buy a 32 bit Windows 10 license.   Are these my only options?     Images  Installation    First run (From the error message I guess it's a 16-bit program)   Clicking on programme "some " vs. "some of " Some of rules can be the same for most websites.   vs.     Some rules can be the same for most websites.   I think I want to say     Some of these rules can be the same for most websites. Connect Java to a MySQL database Is the set of points in the plane whose coordinates are either both irrational, or both rational connected? Linear Discriminant Analysis for $p=1$ I'm studying 'Introduction to Statistical Learning' by James, Witten, Hastie, Tibshirani.   In page 139, of their book, they began by introducing Bayes' Theorem $p_k(X)=P(Y=k|X=x) = \dfrac{\pi_kf_k(x)}{\sum_{l=1}^k \pi_l f_l(x)}$. $\pi$ is not mathematical constant, but denotes the prior probability. Nothing is strange in this equation.   The book claims that it wants to obtain an estimate for $f_k(x)$ that it can plug into the equation given above. To estimate $f_k(x)$, it assumes that is normal. In the one dimensional setting, $f_k(x)=\dfrac{1}{\sqrt{2\pi}\sigma}\exp(-\dfrac{1}{2\sigma^2}(x-\mu_k)^2)$, where $\mu_k$ and $\sigma^2_k$ are the mean and variance for the $k$th class. It is assumed that $\sigma^2_1 = \sigma^2_2 = \cdots = \sigma^2_K$. (I began to get confused from the last statement.)   Plugging $f_k$ into $p_x$, you have this quite messy equation (1) :   $$p_x(k)=\dfrac{\pi_k \frac{1}{\sqrt{2\pi}\sigma}\exp(-\frac{1}{2\sigma^2}(x-\mu_k)^2)}{\sum_{l=1}^K \pi_l \frac{1}{\sqrt{2\pi}\sigma}\exp(-\frac{1}{2\sigma^2}(x-\mu_l)^2)}. $$  Again, no surprises here since it is just substitution.     The Bayes' Classifier involves assigning an observation to the class for which equation (1) is the largest. Taking the log of Equation (1) and rearranging terms, it is not hard to show that this is equivalent to assigning the observation to the class for which the following is the largest:  $$\delta_k(x)=x \cdot \dfrac{\mu_k}{\sigma^2} - \dfrac{\mu_k^2}{2\sigma^2} + \log(\pi_k) $$  Question: I do not understand where this came from, and what it means. I tried doing the log of equation and it doesn't become this. Are we taking the derivative somewhere here, since this is the largest observation? Granting access only to standby database One of the physical standby databases in my environment is open in read-only mode and used for reporting purposes . I want to give users access only to this particular standby, not to primary db.   The best approach I found so far is to create AFTER LOGON ON DATABASE trigger which checks v$instance (or maybe v$database), and throws error for depends on  values of host_name/instance_role columns  .   I wonder if there is a better way to do it.