What is Closed: Definition and 1000 Discussions

In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation.
This should not be confused with a closed manifold.

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  1. M

    Using Index Theory to show a system has no closed orbits

    Homework Statement I'm doing a course in nonlinear dynamics using Strogatz. One of the exercises in the book is "Using index theory show that the system has no closed orbits" Homework Equations \dot{x} = x(4-y-x^{2}) , \dot{y} = y(x-1) The Attempt at a Solution Turns out there...
  2. N

    A single atom in a cold, closed, vacuum system.

    Let us assume there is a single atom in a vacuum chamber which is kept at near absolute zero. Now assume the system is closed and that the chamber is large enough such that the atom cannot diffuse far enough to reach the walls. Neglecting other stochastic effects, what do you think the atom's...
  3. J

    Calculating Steam Pressure in Closed Container

    I am trying to calculate the volume of liquid water i need to place in a sealed container in order to obtain 10 psi of steam pressure in that closed container. Here are the numbers: Temp: 816 C Volume of steel pipe: 154.497 ml Final pressure: 10 psi If I left out a required number...
  4. C

    Find lifetime of closed RD universe

    Homework Statement Integrate field equations for a universe filled with radiation and with k = +1, λ = 0. Find ρ(a) ρ(t) and a(t). Find lifetime of the universe. Homework Equations Use first Friedmann equation which reduces to a'2/a2 + a-2 = kρ where k = 8∏/3 The Attempt at...
  5. Q

    Modal energy distribution in closed pipe resonance

    When one causes the air column in a closed pipe to vibrate in its well-known modes (harmonics) or a plucked string to vibrate similarly, how is the exciting energy distributed amongst the modes?
  6. K

    Could I treat this as a closed loop?

    Could I treat this picture as a closed loop? This is part of a much larger problem, so this is all I need to know. I think I can because the ends go off to infinity, but I'm not sure. http://i.imgur.com/RFCsrqH.jpg
  7. C

    Using Farady's law with a closed loop.

    Homework Statement The figure below shows two circular regions R1 and R2 with radii r1 = 20.0 cm and r2 = 32.9 cm. In R1 there is a uniform magnetic field of magnitude B1 = 52.4 mT directed into the page, and in R2 there is a uniform magnetic field of magnitude B2 = 75.6 mT directed out of...
  8. H

    Closed form for (in)finite sums

    I have a set of questions concerning the perennial sum \large \sum_{k=1}^{n}k^p and its properties. 1. For p \ge 0, the closed form of this is known (via Faulhaber's formula). I know little about divergent series, but I've read that in some sense there exists a value associated with these sums...
  9. A

    Closed ended tube resonance problem

    Homework Statement In class a 3 m long aluminum bar was made to resonate by clamping it at a node in the centre of the bar. The frequency heard was 1200Hz. Homework Equations L = \frac{n}{4}\lambda v = f\lambda The Attempt at a Solution Knowing that L is 3, we can...
  10. K

    Closed form expression of the roots of Laguerre polynomials

    The Laguerre polynomials, L_n^{(\alpha)} = \frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x}x^{n+\alpha} \right) have n real, strictly positive roots in the interval \left( 0, n+\alpha+(n-1)\sqrt{n+\alpha} \right] I am interested in a closed form expression of these roots...
  11. P

    MHB Is the limit vector $x$ in the subspace $F$?

    Let L^2 be the usual vector space of complex sequences. Let F be the subspace of sequences whose first term is zero. Show that F is closed. Let $((V_{nk}):k=1,2,...)$ be a convergent sequence in F. I need to show it converges to a sequence whose first term is 0. Well, for all positive...
  12. D

    Pressure in a closed system using an inclined manometer

    Homework Statement In the figure attached the pressure at A and B are the same 100 kPa. If water is introduced at A to increase p_A to 130 kPa find the new positions of the mercury menisci. The connecting tube has a diameter of 10 mm. Assume no change in Liquid density. Homework...
  13. P

    Normally open switch & Normally closed switch.

    This is not really a homework question. Just a question regarding the normally open (NO) and normally closed switches. For an NO switch, if the button is pressed (not open anymore) and then the button is released, is the switch still in the "not open" state or does it go back to the open state?
  14. H

    Questions about closed timelike curves

    I have read about CTCs from some books and find the explanations confusing. -Are they simply natural trajectories in the given spacetimes? -How is energy-momentum conserved if a particle can simply travel back in time? i.e. Observers will observe particles traveling in a CTC to simply...
  15. G

    Why is the flux through a closed surface zero with no charge inside?

    Hi, I'm trying to teach myself electricity and magnetism (and it's not easy!) and I'm not sure I understand flux... For one thing, why is the flux through a closed surface zero if there is no charge inside of the surface (but there IS one outside)? Another thing I'm not really sure about this...
  16. M

    Linear recurrence = closed form?

    Hi I've got a recurrence relation: x_n = a*x_(n-1) + b; I think I'm going mad trying to figure out a closed form, eg. x(n) = ? the nth iteration Is there a trick or something I'm missing? Thanks
  17. S

    Subspace topology and Closed Sets

    Homework Statement Hi, This is my first post. I had a question regarding open/closed sets and subspace topology. Let A be a subset of a topological space X and give A the subspace topology. Prove that if a set C is closed then C= A intersect K for some closed subset K of X. Homework...
  18. S

    Find the Capacitance when the switch is closed

    Homework Statement When the switch is closed, Potential drops to 40v across C1 & C2(Parallel series). Find the Capacitance of C2 Homework Equations Before switch is closed C1=300uF and holds a charge of Q1=3e4 uC V=100vAfter switch is closed V'=40vThe Attempt at a Solution V1=V2 So...
  19. B

    Is S a closed subset of ℝ^n if it is compact?

    Theorem: Let S be a compact subset of ℝ^n. Then S is closed. Before looking at the book I wanted to come up with my own solution so here is what I've thought so far: Fix a point x in S. Let Un V_n (union of V_n's...) be an open covering of S, where V_n=B(x;n). We know that there is a...
  20. V

    How Do You Calculate K for a Closed Loop Damping Ratio in Higher Order Systems?

    From control systems: I am asked to find the value of K that gives the closed loop damping ratio of 1/sqrt2. The value for the complimentary sensitivity is T(S)=(2KS +4K)/(s^3 +162S^2 +(320+2K)S +4K) so how do I find the value for K? I tried putting it in the general equation, but it...
  21. alyafey22

    MHB Find a closed form interpretation for the integral :

    $\displaystyle \int^{\infty}_0 \, \frac{\log (1+e^{ax})}{1+e^{bx}}\, dx $ I am not sure whether it can be solved :confused:
  22. Y

    Water speed in the closed system

    Does water speed in the pipes having the same diameter is strictly the same in any point of a closed (heating) system (with pump working) ? On the contrary, although liquids are "incompressible" in practice, however, does the piping still allows it to be so : the more far the water from the...
  23. G

    Proving {x} is a closed set in a metric space

    Hi everyone, I posted this a couple days ago and didn't get a response, so I thought I'd try again. Let me know if something about this is confusing. Thanks! Homework Statement Let X be a metric space and let x\in{X} be any point. Prove that the set \left\{x\right\} is closed in X...
  24. F

    Are measurable sets open or closed?

    I'm seeing the term "measurable sets" used in the definition of some concepts. But when comparing with other concepts that rely on "closed sets", I can't seem to easily find whether measureable sets are open or closed. Does anyone have any insight into that? Thanks.
  25. B

    Acceleration in a Closed Box: Uniform or Varied?

    It's said that it is not possible to tell the difference between acceleration of objects within a closed box and acceleration due to gravity. Is this allways the case.Does the acceleration of objects within a closed box act uniformly or does this depend on the gradual acceleration of the...
  26. dexterdev

    Current flows only when circuit is closed, right? but for antennas

    Hi pf, I thought that current will flow in closed loops only , but the figure attached shows working of antenna with current in open circuit, but how? :confused: -Devanand T
  27. C

    Help understanding closed line integrals

    Hi I'm currently studying Electromagnetism, and we keep coming across this symbol: \oint A closed line integral, something I have never really been able to understand. If a normal integral works like this: http://imageshack.us/a/img109/3732/standardintegral.png where f(x) is the "height"...
  28. B

    Small oscillations and closed orbit

    Homework Statement I'm studying small oscillations. When can I say that an orbit is closed? The Attempt at a Solution I remember that there is a ratio that must be a rational number but I don't remember other thing... Thank you!
  29. B

    Proof that a given subspace of C[−1,1] with L2 norm is closed

    Homework Statement Let H= C[-1,1] with L^2 norm and consider G={f belongs to H| f(1) = 0}. Show that G is a closed subspace of H. Homework Equations L^2 inner product: <f,g>\to \int_{-1}^{1}f(t)\overline{g(t)} dt The Attempt at a Solution I've been trying to prove this for a...
  30. Solarmew

    What happens when the switch is closed in a 555 timer and left there?

    Here's my circuit The question at hand is what happens when the trigger switch is closed during the timing cycle (after being closed once already to initiate said cycle) here's the waveform I'm getting, but I'm not sure what to make of it. could someone please help me understand...
  31. E

    Closed form solutions to integrals of the following type?

    For any integral where the integrand is of the form f(θ)^z, with z a complex number, and f(θ) = sin(θ), cos(θ), tan(θ), ... etc., θ being either real or complex. Is it possible to explicitly solve for an antiderivative? I'm not aware of any such way I could use residues/series representations...
  32. J

    Show that the system has no closed orbits by finding a Lyapunov

    Show that the system has no closed orbits by finding a Lyapunov ... Homework Statement I'm at the point in the problem where I need constants a and b satisfying ax2(y-x3) + by2(-x-y3) < 0 and ax2+bx2 > 0 for all (x,y)≠(0,0). Homework Equations Just in case you're wondering...
  33. T

    Waves in air in a tube that is closed

    1. The air in a closed pipe with an adjustable plunger in is made to vibrate at a frequency 256 Hz over its open end. As the length of the pipe is increased, loud notes are heard as the standing wave in the pipe resonates with the tuning fork. (a) What is the shortest length that will cause a...
  34. E

    Is directional gas flow possible in a circular closed pipe system?

    If I have a series of pipes and containers (containing liquid) soldered together to create a circular path, and then heated at a particular point or multiple points, is it possible to somehow have the gas move in a particular direction without the gas every leaving the system? I'd prefer not to...
  35. Fantini

    MHB Continuity in terms of closed sets

    Hello. I wish to prove this: $$\text{A function } f: X \to Y \text{ is continuous if and only if the inverse image of any closed set is closed.}$$ Proof: $(\implies)$ Let $V \subset Y$ be a closed se. By definition, $Y-V$ is an open set, and by the continuity of $f$ it follows that...
  36. E

    Current Through a Capacitor after switch closed

    http://imgur.com/PQ4XCEo 2.V=IR 3. I know the capacitor has a voltage of 5.5 because it is charged to the supply voltage, I don't understand what happens to current when the switch is opened.
  37. F

    Question about infimums and closed sets

    Homework Statement So this question arose out of a question about showing that a set χ is dense in γ a B* space with norm ||.||, but I think I can safely jump to where my question arises. I think I was able to solve the problem in another way, but one approach I tried came to this crux and I...
  38. S

    Complex Integration over a Closed Curve

    (a) Suppose \kappa is a clockwise circle of radius R centered at a complex number \mathcal{z}0. Evaluate: K_m := \oint_{\kappa}{dz(z-z_0)^m} for any integer m = 0, \pm{1},\pm{2}, ,... Show that K_m = -2\pi i if m = -2; else : K_m = 0 if m = 0, \pm{1}, \pm{2}, \pm{3},... Note...
  39. L

    Closed subspace of a Sobolev Space

    Homework Statement I am considering the space \tilde{W}^{1,2}(\Omega) to be the class of functions in W^{1,2}(\Omega) satisfying the property that its average value on \Omega is 0. I would like to show that \tilde{W}^{1,2}(\Omega) is a closed subspace of W^{1,2}(\Omega). Homework...
  40. C

    Examples of closed loop functions

    Can someone please give me a list of examples of closed loop functions, the only one I know is the equation for a circle y^2 + x^2 = r^2 Also are there any closed loop functions that aren't multi variable, i.e in the form y=f(x) and not z=f(x,y) Is there a way to tell that a function is...
  41. G

    Closed and Open Subsets of a Metric Space

    Homework Statement Let X be an infinite set. For p\in X and q\in X, d(p,q)=1 for p\neq q and d(p,q)=0 for p=q Prove that this is a metric. Find all open subsets of X with this metric. Find all closed subsets of X with this metric. Homework Equations NA The Attempt at a...
  42. D

    Closed electron configuration equivalent to closed shell

    "closed electron configuration" equivalent to "closed shell" Hi, is the term "closed electron configuration" equivalent to "closed shell"? derivator
  43. N

    Is a Closed, Adiabatic Device Feasible For Work With Steam?

    2. A closed, adiabatic device claims to derive useful work by expanding 1 kg of steam from 500 C and 20 bar to 100 C and 1 bar. Do you believe this claim? Assume steam is a real fluid following the steam tables in Appendix A.III.
  44. B

    A Closed set in the Complex Field

    This is elementary but surely this set is closed | c – i | ≥ | c | with c being in ℂ I am trying to picture the set. Is it outside the disc centered at (0,1) with radius equal to modulus c (whatever that is) ? Thanks
  45. N

    Thermodynamic Reversible/Irreversible Closed Systems

    I am completely lost with this problem. How would I go about breaking it up into manageable components that so I won't get lost in the problem? Homework Statement A 2 m3 rigid storage tank containing 10 kg of steam is heated from 300 to 400 C by transferring heat from a hot reservoir at...
  46. Ibix

    Closed flat space twin paradox

    I'm not sure if this belongs here or in Cosmology - possibly either would do, I think. I was reading the thread about open/closed/flat universes that's currently ongoing in Cosmology, and a related question occurred to me. According to post #7 you can have geometrically flat universes that...
  47. B

    What is a Closed Form for the Sequence?

    Homework Statement Let Ʃ 1\(n^2-1) from n=2 to k. It says find a closed for it and prove it using sum notation. Homework Equations The Attempt at a Solution I can easily prove it by induction but I don't know what a closed form means. I tried looking it up online but there really...
  48. D

    Meaning of a Flat, Open, and Closed Universe

    Meaning of a "Flat," "Open," and "Closed" Universe Hello all, I'm reading up on cosmology and the potential shapes of the universe based on its density in relation to the critical density. When one says that a universe is "flat," what precisely does this mean? Does this mean that the...
  49. B

    An Open and Closed Interval in Q

    Why is the interval ##(-√2,√2)## closed in ##\mathbb{Q}## I know why it is open, but do we consider it closed because it has no limit points in ##\mathbb{Q}##, thus vacuously it is closed.
  50. A

    When is the kernel of a linear operator closed?

    If you consider a bounded linear operator between two Hausdorff topological vector spaces, isn't the kernel *always* closed? I mean, if you assume singleton sets are closed, then the set \{0\} in the image is closed, so that means T^{-1}(\{0\}) is closed, right (since T is assumed continuous)? I...
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