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. J

    MHB Every Closed Set in R has a Countable Dense Subset

    Show that every closed set in R has a countable dense subset. Let's call the set F. I've been thinking about this problem for a little bit, and it just doesn't seem like I have enough initial information! I tried listing some things that I know about closed sets in R: $\cdot$ Countable...
  2. vilasini

    Closed trajectory of a wormhole

    Homework Statement I have a metric for wormhole. Now if I want to find the closed trajectory for this metric how will I proceed from here? Help me with detailed maths if possible. Homework EquationsThe Attempt at a Solution
  3. TheQuestionGuy14

    B Are Geometries that contain Closed Timelike Curves Possible?

    Some exact solutions to Einstein's General Relativity show that Closed Time like Curves may theoretically exist. Could they actually exist in our universe? And if so, how would it change the understanding of physics and our universe?
  4. Highwire

    [The Theoretical Minimum] Can closed systems exist?

    Homework Statement The first exercise in Susskind and Hrabovsky's The Theoretical Minimum is one that, in the words of Susskind, "is designed to make you think, more than it is designed to test you." The exercise asks: Homework Equations In the prior paragraph, the authors define the notion...
  5. S

    Waves in a closed organ pipe (homework check)

    Homework Statement A closed organ pipe of length 1.00m is filled with a gas and is found to give the same note as an open pipe of length 1.30m filled with air, when both are resonating at their fundamental mode of vibration a) draw diagrams to show the nature of the waves in each pipe and use...
  6. G

    Engineering Electrical circuits: when all switches are closed, what is R?

    Homework Statement https://pasteboard.co/Hj3g5Km.jpg When both switches 1 and 2 are closed,what is the total resistance of the set up? I couldn't figure out which resistors are connected in parallel and which resistors are actually in series in this set up when both swtiches are closed. I...
  7. T

    MHB Simple closed form for integral

    How may we go about to show that, $$\int_{0}^{1}t\cos(2t\pi)\tan(t\pi)\ln[\sin(t\pi)]\mathrm dt=\color{green}{1\over \pi}\cdot\color{blue}{{\ln 2\over 2}(1-\ln 2)}$$
  8. Maria

    Simple closed force system -- Mechanics

    Homework Statement There is a system of 4 points located along a circle of radius R. Points are connected by undeformable ropes (pink on the picture). There is a force applied to each point. Scheme: https://we.tl/MsCEViCQdB I need to find resulting force in the system. The Attempt at a...
  9. T

    MHB A hard integral gives a simple closed form, π/(4a)^3

    Proposed: How can we prove $(1)?$ $$\int_{0}^{\infty}\mathrm dx{\sin^2\left({a\over x}\right)\over (4a^2+x^2)^2}={\pi\over (4a)^3}\tag1$$
  10. SSGD

    I Area between two closed curves

    I have been trying to find an answer to this problem for some time. So I was hoping the community might be able to point me in the right direct. https://drive.google.com/open?id=1Y2hYkRG94whLroK20Zmce07jslyRL3zZ I couldn't get the image to load. So above is a link to an image of the problem...
  11. A

    I Integrating a Function over a Torus Contour

    I'd like to integrate a function over a closed circle-like contour around an arbitrary point on a torus and I assume I would use the expression: $$ \int_{t_1}^{t_2} f(x,y,z) \sqrt{x'(t)^2+y'(t)^2+z'(t)^2}dt$$ And I cannot come up with an explicit parameterization of the variables in terms of...
  12. A

    I Cavitation in a closed loop pumping system

    Dears Kindly, I want to hear from you regarding this topic. The system is closed cooling system. I believe it is difficult to attribute the sound you hear from centrifugal pump to be a cavitation especially if the discharge pressure is normal. The last time we had a problem with this system...
  13. Muhammad Usman

    What is the Significance of the Electric field in a closed circuit

    Hi, I am confused about the electric field lines which are depicted mostly on the Internet as per conventional way. What I understand that the conventional current was due to positive charges which was wrong. Actual flow of the current was due to the negative charges or electrons. When the...
  14. Eclair_de_XII

    Proof for convergent sequences, limits, and closed sets?

    Homework Statement "Let ##E \subset ℝ##. Prove that ##E## is closed if for each ##x_0##, there exists a sequence of ##x_n \in E## that converges to ##x_0##, it is true that ##x_0\in E##. In other words, prove that ##E## is closed if it contains every limit of sequences for each of its...
  15. M

    Heat transfer from a closed cylinder filled with fluid

    I have a long steel uninsulated cylinder filled with hydraulic fluid (let's say it's mineral oil), and I need to figure out how many barrel heaters to clamp onto it in the winter months to prevent the steel surface temperature from dropping under 40 degrees Fahrenheit. My question is, how do I...
  16. Rohan de Silva

    I Delayed Choice with both slits closed, What happens?

    I am reading about this most famous experiment in physics, the double-slit experiment. My question is very simple: in the "Delayed Choice" version, have they done the test where they close BOTH SLITS (at once) after the photon has passed the slits?? If so, what have been the result? Can you...
  17. F

    Electric Flux in a Closed Space: Volume, Area & Benefits

    I believe the electric flux within a closed space can be found with the equation phi = Q/ε0. Can this be used for volume and area, or just volume? Also what good does this do. Why would I want to know the electric flux of something?
  18. BiPi

    A Why a Lie Group is closed in GL(n,C)?

    The Brian Hall's book reads: A Lie group is any subgroup G of GL(n,C) with the following property: If Am is a secuence of matrices in G, and Am converges to some matrix A then either A belongs to G, or A is not invertible. Then He concludes G is closed en GL(n,C), ¿How can this be possible, if...
  19. Math Amateur

    MHB Another question on Open and Closed in V .... D&K Proposition 1.2.17 .... ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with another aspect of the proof of Proposition 1.2.17 ... ... Duistermaat and Kolk's Proposition 1.2.17 and the preceding...
  20. Math Amateur

    MHB Open and Closed in V .... D&K Proposition 1.2.17 .... ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of the proof of Proposition 1.2.17 ... ... Duistermaat and Kolk's Proposition 1.2.17 and the preceding...
  21. Math Amateur

    MHB Compact Sets and Closed Sets in R^n .... .... D&K Lemma 1.8.2 .... ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of the proof of Lemma 1.8.2 ... ... Duistermaat and Kolk"s Lemma 1.8.2 and the preceding definition and notes...
  22. B

    How long after the switch is closed does the voltage across

    Homework Statement Consider the circuit How long after the switch is closed does the voltage across the resistor drop to Vf = 20V. Answer in units of s. Homework Equations Tc = RC Q=Qm(1-e-t/RC) The Attempt at a Solution [/B] RC = .0003026 11 = 31(1-e-t/RC) .3548 = 1-e-t/RC 1.3548 =...
  23. TheQuestionGuy14

    B How can Closed Timelike Curves be made?

    Hey. I really like the topic of Closed Timelike Curve's, they're an interesting subject matter, since they're allowed by certain field equations of GR. I was curious if there is any way (in the future?) we could warp spacetime to create a CTC, and maybe harness it? Could be useful.. ish. Thanks.
  24. Richie Smash

    Explain How the Lamp in Circuit A Lights When Switch S is closed

    Homework Statement Hello Everyone, a pleasant good morning to all :) I will attach an image that shows a diagram of a circuit. The question based on this picture is as follows: ''When switch S is closed, the Lamp L, lights. Explain how this occurs.'' Homework EquationsThe Attempt at a Solution...
  25. Math Amateur

    MHB The Closure of a Set is Closed .... Lemma 1.2.10

    I am reading "Multidimensional Real Analysis I: Differentiation by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of the proof of Lemma 1.2.10 ... Duistermaat and Kolk"s proof of Lemma 1.2.10 (including D&K's definition of a...
  26. Faefnir

    Magnetic field in a closed path

    Homework Statement Find (a) the module and (b) the direction, entering or exiting the page plane, of the magnetic field at point P, knowing that a = 4.7 cm and i = 13 A Homework Equations Biot-Savart law The Attempt at a Solution For 1-2 and 4-5 segments, B = 0 because sin θ = 0 for...
  27. nothing909

    Expression for closed loop gain of differential amplifier

    Homework Statement The question is Derive an expression for the closed loop gain of the differential amplifier. I have solutions for these questions but the solution for this question is quite vague. Here is the solution: I understand part 1 and part 3, but part 2 I don't. So looking at...
  28. L

    B Confusion about closed timelike curves

    [Moderator's note: split off from another thread since this is a separate topic.] I am confused about closed timelike curves. To say that they are possible using an exact solution to the EFEs, like the Godel metric, and that they actually correspond to something in reality is where my confusion...
  29. G

    Body describes a closed trajecty on a free-to-spin disk

    [Moderator's Note: Thread title changed to better reflect the problem statement] Homework Statement A body of mass m is on a disk of mass M=2m and radius R, initially static and free to spin around its center. The mass mm goes around a trajectory described in the image below with constant...
  30. J

    Fluid Velocity and Pressure in a *Closed* System

    In a closed fluidic system (with a pump), fluid velocity is constant throughout the system but what puzzles me is the pressure drop due to viscous effect. In a horizontal pipe, pressure decreases gradually (assuming low friction) down the pipe due to viscous effect. In this concepts, it's hard...
  31. C

    B Node at a closed end and an antinode at a open end of a tube

    What causes there to be a node at a closed end of an air column and an antinode at the open end of a air column? Why doesn't it change as the wave oscillates?
  32. M

    Closed container vs Open container for calorimetry

    So let's say I do the reaction Mg + HCl --> MgCl2 + H2 in an open calorimeter. I measure a certain temperature change in the calorimeter, let's say an increase of 12 degrees C. Keeping all other variables the same, if I perform this experiment in a closed calorimeter, what will happen to the...
  33. L

    Predicting the behaviour of a closed circular airfoil

    I was out and about today and observed a dog walker playing frisbee with their dog. I noticed the frisbee gliding gracefully through the air as the dog jumped to grab it, clutching the ring-like disc in its mouth. It got me to thinking about airflow over the disc, the lift and drag properties...
  34. lfdahl

    MHB Derive a closed form and find its limit

    Let $S_n(k)$ be defined by: $S_n(k) = 1 + 2k+3k^2+...+(n+1)k^n$, where $|k| < 1$ and $n \in \Bbb{N}$. Derive a closed form for $S_n(k)$ and find the limit: $$\lim_{{n}\to{\infty}}S_n(k)$$.
  35. PsychonautQQ

    I Proof that retract of Hausdorff space is closed

    I'm reading this proof on the matter: https://math.stackexchange.com/questions/278755/show-that-a-retract-of-a-hausdorff-space-is-closed How do we know that the final neighborhood they come up with is disjoint from A?
  36. Mr Davis 97

    Show that lim S is a closed set

    Homework Statement Suppose that pn → p and each pn lies in lim S. We claim that p ∈ lim S. Since pn is a limit of S there is a sequence (pn,k)k∈N in S that converges to pn as k →∞. Thus there exists qn = pn,k(n)∈ S such that d(pn, qn) <1/n. Then, as n→∞ we have d(p, qn) ≤ d(p, pn) + d(pn, qn) →...
  37. Mr Davis 97

    Prove that the complement of a closed set is open

    Homework Statement Suppose that S is a closed set. We claim that Sc is open. Take any p ∈ Sc. If there fails to exist an r > 0 such that d(p, q) < r ⇒ q ∈ Sc then for each r = 1/n with n = 1, 2, . . . there exists a point pn ∈ S such that d(p, pn) < 1/n. This sequence in S converges to p ∈ Sc...
  38. R

    Kalman filter unstable in closed loop application

    I have implemented the closed-loop motor control system as above in a Matlab simulation (pic Kalman.png). Here, the Kalman filter estimates the torque disturbance and angular speed of the motor and those are feed to the RLS algorithm for parameter identification, here it estimates the combined...
  39. B

    Extending a Continuous Function a Closed Set

    Homework Statement Let ##E## be a closed set of real numbers and ##f## a real-valued function that is defined and continuous on ##E##. Show that there exists a function ##g## defined and continuous on all of ##\Bbb{R}## such that ##f(x) = g(x)## for each ##x \in E##. Homework EquationsThe...
  40. D

    What is the pressure in a closed container dependent on?

    Hello! I have a problem : I have an elastic container (I call it "balloon"). I fill it 100% with water (no air bubbles) and close it. There is a pressure sensor connected to the balloon to measure the pressure inside it. I would like to ask You : what factors have influence on the pressure...
  41. Math Amateur

    MHB Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (3) ... ... Exercise 2.2.4 Part (3) reads as follows: I am unable to make a meaningful...
  42. Math Amateur

    Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3 ....

    Homework Statement I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (3) ... ... Exercise 2.2.4 Part (3) reads as follows: Homework...
  43. Math Amateur

    MHB Closed Sets - Sohrab Exercise 2.2.4 - Part 2

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (2) ... ... Exercise 2.2.4 Part (2) reads as...
  44. L

    Can a 2500 Gallon Water Tank Sufficiently Cool a Condenser Without a Chiller?

    Hello! Hopefully someone here can help with this problem: I have a condenser that holds 35 gallons of water to cool the copper coil on my still. I need to know if I can create a closed loop system of cooling water that allows me to avoid running a chiller. I know that there is probably an...
  45. DaveC426913

    B Knot theory: closed loops in n dimensions

    I'm not a math machine, but I dabble in dimensional stuff. I think this falls under knot theory. I have built several prototypes of a tesseract. Each of them sits in a little case in my office. One of them is made from truncated cubes, held together with elastic cord: In theory, the...
  46. H

    Partially closed pump discharge valve question

    Hi all, I have a question about the effect of partially closing a pump discharge valve on the system curve, wondering if you guys can help me out. Right now I have the yellow pump curve and the orange 2 inch system curve , producing around 120 gpm against around 110 ft of head. If I expand...
  47. A

    I Prove that solid angle of any closed surface is 4pi

    I googled a lot on proof of Gauss theorem and nearly every other proof (on web and so on books) state that solid angle of closed surface is 4pi but I can't find the proof of this nowhere ! I tried setting up the integral but don't know how to proceed furthur : Ω=∫(cosθ/r^2)*dA Also The one...
  48. davidge

    I Proving non homeomorphism between a closed interval & ##\mathbb{R}##

    I was trying to show that a closed interval ##[a,b]## and ##\mathbb{R}## cannot be homeomorphic. I would like to know whether this can actually be considered as a proof. It is the following: - The closed interval ##[a,b]## can be written as ##[a,p] \cup [p,b]##, where ##a \leq p \leq...
  49. acvtre

    HVAC DIY glovebox or closed fume-hood?

    Hi everybody, I'm a PhD student working on solution-processed kesterite PV cells. The material is spin-coated and I personally believe that its wetting properties are influenced by environmental parameters like temperature and humidity. To control these parameters, or at least reduce their...
  50. Hiero

    B Special relativity implies the space cannot be "closed"?

    I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location. Suppose there is an observer S on a planet and an observer S'...
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