It may be an odd question.  But, I particularly want to know the open's of cantor set with inherited topology of real line.
Does anyone know of any interesting subsets of the Cantor set? When I first started thinking about this, I thought that since the Cantor set $C$ is the intersection of disjoint unions of closed sets, those particular closed sets would be subsets of $C$. Those sets, however, happen to be intervals! The Cantor set contains no isolated points nor (open) intervals, so then what subsets does it contain besides $\varnothing$ and itself?
Integral of $\frac{1}{x^4+1}$ Just doing this for revision, seems much harder than it should be, should I use $x=\tan u$ ? Any help appreciated. Visiting USA as a German with Iranian parents 99% of the time, I'm clear on when I should use "a" versus "an." There's one case, though, where people &amp; references I respect disagree.  Which of the following would you precede with "a" or "an," and why?   FAQ FUBAR SCUBA   [Note: I've read the questions  and , but the rules given there don't necessarily apply here.]    [Edited to add]  Here's a shorter (and hopefully clearer) version of the question…  In written English, which is correct (and why): "a FAQ" or "an FAQ"?  Some references with differing opinions:   an: the  and  a: the Microsoft Manual of Style for Tech Publications, 3e either: the  and Wouldn't the use of WayneTech by Bane fully expose Bruce Wayne's identity as Batman? What is the relationship between symmetry and degeneracy in quantum mechanics? Let me remind you about the following classical  examples in quantum mechanics.     Example 1. Bound states in 1-dim potential V(x).   Let $V(x)$ be a symmetric potential i.e.   $$V(x) = V(-x)$$   Let us introduce the parity operator $\hat\Pi$ in the following way:   $$\hat\Pi f(x) = f(-x).$$   It is obvious that    $$[\hat H,\hat\Pi] = 0.$$   Therefore, for any eigenfunction of $\hat H$ we have:   $$\hat H|\psi_E(x)\rangle = E|\psi_E(x)\rangle = E\hat\Pi|\psi_E(x)\rangle,$$   i.e. state $\hat\Pi|\psi_E(x)\rangle$ is eigenfunction with the same eigenvalue. Is $E$ a degenerate level? No, because of linear dependence of $|\psi\rangle$ and $\hat\Pi|\psi\rangle.$   Consider the second example.     Example 2. Bound states in 3-dim a potential $V(r)$. Where $V(r)$ possesses central symmetry, i.e. depends only on distance to center.   In that potential we can choose eigenfunction of     angular momentum $\hat L^2$ for basis    $$|l,m\rangle,$$   where $l$ is total angular momentum and $m$ - its projection on chosen axis (usually $z$). Because of isotropy eigenfunction with different $m$ but the same $l$ correspond to one energy level and linearly independent. Therefore, $E_l$ is a degenerate level.      My question is if there is some connection between symmetries and degeneracy of energy levels. Two cases are possible at the first sight:   Existence of symmetry $\Rightarrow$ Existence of degeneracy Existence of degeneracy $\Rightarrow$ Existence of symmetry     It seems like the first case is not always fulfilled as shown in the first example. I think case 1 may be fulfilled if there is continuous symmetry. I think the second case is always true. I would like to work out the Fourier transform of the Gaussian function   $$f(x) = \exp \left(-n^2(x-m)^2 \right)$$  It seems likely that I will need to use differentiation and the shift rule at some point, but I can't seem to get the calculation to work. Does anyone have any advice?  By the way, I am using   $$\mbox{FT}(f)(k)=\int_{-\infty}^\infty f(x)e^{-ikx}\,\mathrm d x$$  as my definition of a Fourier transform. Many thanks. How to remove the Mail icon indicator applet? How do I distinguish between a command, utility, or builtin for getting documentation? I'm running Bash scripting, but sometimes I get confused which of these commands I use belong to who. Sometimes man xxx works, sometimes doesn't, so I use --help or info, mostly one of these works to show description of the command. Can anyone tell me how I would know what command belongs to what? Bash builtin, GNU utility, etc. is there any extra latency using an amp sim on wine? I want to use AmpliTube amp sim on ubuntu studio but there isn't a linux version for it, can I just use wine and will it have any extra latency? if so how much latency? Flag as Broken Link I keep finding broken links in posts, currently I add a comment in the hope someone will return to update it or if I find a link I edit the answer.   I imagine this will only increase over time so I wonder if there could be a standard way to manage this?  My idea is adding a new flagging reason like "contains broken links", then it will go to a review queue where people will be able to have a look and fix the broken links. Is there an expression to indicate the strategy of wearing someone down with numerous small irritations? I would use rope-a-dope, but it's got connotations of pretending to lose that I don't need. I'm trying to describe the behavior of someone who sends twenty detailed emails a day about various projects, and the recipient of his emails has finally gotten tired of trying to parse them, so the recipient just agrees to whatever he proposes. I'd like an expression that evokes both outward earnestness and hidden creepiness, like Uriah Heep, Dickens's "Humble servant" with veiled ambition, who overdoes it with professions of humility until he's in power. Water torture would work, but comes too close to a more racist expression that I'm not comfortable with. Router to router setup works fine with straight cable up to 2-3 meter it is not working for 45 meter why? Why is the method executed immediately when I use setTimeout? Blender Internal glossy BSDF equivalent? How do you use unlocked rewards after each mission in Splinter Cell: Double Agent? In the PC version of Splinter Cell: Double Agent, how can you use the rewards that you receive after each mission? For example, the shotgun attachment, or the colored night vision?  My list shows that the rewards are there, but I can not figure out how to use them. When should I publish in interdisciplinary versus subject-specific scientific journals? Simple UV Mesh Unwrapping Scale issue Comment submission broken for comments that end with @username No space following macro without argument With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space? Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$