Closed Definition and 1000 Threads

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. A

    Effects of Wings in a closed environment

    I was wondering if somebody could let me know if wings inside of a closed environment (tube of sorts) with air flowing over them would generate lift, or if the air flowing over them would be directed downwards onto the bottom of the tube, canceling any lift generated by the wings? The first...
  2. Z

    Closed form integral of abs(cos(x))

    Hi everyone. Recently, I came across a closed form solution to ∫|cos(x)|dx as sin(x-∏*floor(x/∏+1/2)) + 2*floor(x/∏+1/2) I have no idea how to reach this solution but checking this for definite integral from 0 to 3∏/4 or ∏ seems to work. Using |cos(x)| as cos(x)*sgn(cos(x)) doesn't...
  3. S

    Why Is Infinite Degrees of Freedom Important for Thermal States?

    Are electrons closed systems?
  4. P

    Simulating Closed Timelike Curves through Quantum Optics

    This paper experimentally simulates Closed Timelike Curves (CTC) through quantum optics experiment. Since I have no experience/background in this, I found it hard to understand how exactly the CTC is implemented in the circuit. [Note: I do understand QM, so no need to explain this].
  5. D

    Mass required for a closed universe.

    How much mass (percentage increase) would have to be added to the Milky Way (our Galaxy) for it to become a closed universe if there were no other mass? Assuming of course the other universal mass does not change some basic physical law. I know a closed universe as a hole is lacking in mass...
  6. J

    Closed integration of exact form

    If ##\omega## is an exact form ##( \omega = d\eta )## and ##\Omega## is the region of integration and ##\partial \Omega## represents the boundary of integration, so the following equation is correct: $$\\ \oint_{\partial \Omega} \omega = 0$$?
  7. D

    If f is analytic on the closed disc

    Homework Statement If f is analytic on the closed disc, show that for r<1 we have f(re^{i\phi}) = \frac{1}{2\pi} \int_{0}^{2\pi}\frac{f(e^{i\theta})}{1-re^{i(\phi - \theta)}}d\theta Homework Equations The Attempt at a Solution I tried using cauchy integral formula and end up...
  8. Y

    MHB Min-Max over a closed bounded region

    Hello again I have another question regarding absolute min-max over a region. This is a weird one. My function is: \[f(x,y)=x^{2}+y^{2}-xy\] and the region is: \[\left | x \right |+\left | y \right |\leq 1\] Now, I have plotted the region using Maple: The answer in the book where it...
  9. K

    Control Bandwidth & Closed Loop Bandwidth Meaning?

    Can anyone tell me if Control bandwidth and closed loop bandwidth means the same thing? If not what does control bandwidth mean? Please & Thank you!
  10. Chronos

    Closed Universe? Local H0 Measurements & Relativistic Corrections

    In this paper; http://arxiv.org/abs/1405.7860, What is the distance to the CMB? How relativistic corrections remove the tension with local H0 measurements, it is suggested cosmological distance may be miscalculated due to failure to take into account systematic accumulation of lensing effects...
  11. A

    Nested sequence of closed sets and convergence in a topological space.

    Homework Statement Let ##X## be a topological space. Let ##A_1 \supseteq A_2 \supseteq A_3...## be a sequence of closed subsets of ##X##. Suppose that ##a_i \in Ai## for all ##i## and that ##a_i \rightarrow b##. Prove that ##b \in \cap A_i##. Homework Equations The Attempt at a Solution...
  12. B

    Check that a set is closed, and that another is compact

    I have a problem with this excercise. Ironically I think I can manage the part that is supposed to be hardest, here is the problem: Let (V,||\cdot||), be a normed vector-space. a), Show that if A is a closed subset of V, and C is a compact subset of V, then A+C=\{a+c| a \in A, c \in C\} is...
  13. U

    MHB Proving that a certain closed interval exists

    Let $a$, $b$ be reals and $f: (a,b) \rightarrow \mathbb{R}$ be twice continuously differentiable. Assume that there exists $c \in (a,b)$ such that $f(c) = 0$ and that for any $x \in (a,b)$, $f'(x) \neq 0$. Define $g: (a,b) \rightarrow \mathbb{R}$ by $\displaystyle g(x) = x -\frac{f(x)}{f'(x)}$...
  14. R

    Pump head requirement: Closed vs Open loop

    If a pump pumps water to a heat exchanger at a certain height, say, 20 m is the head required indeed lower for a closed loop system than an open loop system? The link below says so, but I wanted to verify. Assume pipe friction losses are the same in both cases. Can one really take credit for...
  15. P

    Closed Systems and Isolated Systems

    Within the scope of classical mechanics, what exactly is the definition of a closed system, and of an isolated system? Also, do these definitions differ in thermodynamics? And does the law of conservation of linear momentum apply to a closed system or an isolated system?
  16. O

    Is every smooth simple closed curve a smooth embedding of the circle?

    Suppose I have a smooth curve \gamma:[0,1] \to M, where M is a smooth m-dimensional manifold such that \gamma(0) = \gamma(1), and \hat{\gamma}:=\gamma|_{[0,1)} is an injection. Suppose further that \gamma is an immersion; i.e., the pushforward \gamma_* is injective at every t\in [0,1]. Claim...
  17. D

    Is Our Universe Closed or Open? A Thought Experiment at Near-Light Speeds

    If I am understand correctly a moving mass has more energy than a stationary mass. Mass and energy are two forms of the same thing so more mass is more energy and more energy is more mass. Suppose we decided to take our (almost) light speed rocket ship and reach the edge of this apparently...
  18. C

    MHB Inverse map is closed under complementation

    f^-1 (E^c) = (f^-1(E))^c where f is map from X to Y and E is in Y. Prove equality is true.
  19. N

    MHB Why is sin(3pi/2) not equal to 1?

    What exactly does it mean for something to be closed under addition. most of the examples and questions i have gone past, are answered with u + v = u1+v1, ... , u_n + v_n and hence this is closed under addition. So i tried looking for examples where something was not closed under addition...
  20. T

    Magnetic Flux through a Closed Surface

    Homework Statement Using the divergence theorem, evaluate the total flux of a magnetic field B(r) across the surface S enclosing a finite, connected volume of space V, and discuss its possible dependence on the presence of an electric field E(r). Homework Equations ∇.B=0 The...
  21. M

    On Fundamental Closed String Solutions

    I am doing a project on string theory and my first task is to work out fundamental string solution from the I(10) string action in NS sector.I am following A.Dahbolkar, G.Gibbons, J.A.Harvey & F.Ruiz Ruiz, Nuclear Physics B340 (1990) 33—55. Why is it called fundamental string? I have not taken...
  22. R

    Does a wire in a closed circuit induce a voltage on itself?

    According to Faraday's Law a changing magnetic field induces an electric field, an example of this is if you have a wire close enough to another wire with current flowing through it the first wire will also have current run through it because of the induced electric field by the second wire...
  23. 2

    Controlled system - Closed loop system

    I have this assignment (First problem - exercise 2 - dias 7) http://site.iugaza.edu.ps/bhamed/files/2010/02/L4-Root-Locus.ppt Which i am having some problems solving. I am stuck at B) So far i tried to solve the problem, by calculating the distance from origin to the breakaway point, by...
  24. V

    Why doesn't an inductor act as a closed circuit to AC?

    I understand that an inductor acts as a closed circuit to DC because it's just a coiled wire but why doesn't it act the same way for AC? What does it act as in AC?
  25. Y

    MHB How the charge is conserved in a closed loop circuit?

    How the charge is conserved in a closed loop circuit?
  26. M

    MHB Closed infinite orthonormal system

    Hey! :o I am lokking at the proof of the following sentence. An infinite orthonormal system $\{e_1, e_2, ... \} \subset H$, where $H$ an euclidean space, is closed at $H$ iff $ \forall x \in H$ $$||x||^2=\sum_{i=1}^n{|(x,e_i)|^2}$$ We suppose a subspace of $H$, that is produced by the basis...
  27. K

    Closed ball is manifold with boundary

    I've been trying to prove that the closed unit ball is a manifold with boudnary, using the stereographic projection but I cannot seem to be able to get any progress. Can anyone give me a hint on how to prove it? Thanks in advance :)
  28. Y

    MHB Solve Recurrence Relation w/ 3 Terms & Initial Conditions

    How to solve this question. Please explain step by step.
  29. W

    The a set is open iff its complement is closed?

    Around the 4 minute mark the lecturer makes this statement, but I am not convinced this is true. I accept that (1) if a set is closed, its complement is open. but consider the converse. Consider an open ball S of some arbitrary radius centered at the origin (in whatever dimension d...
  30. N

    H20, CO2 and O2 in a Closed Container for a Long Time

    How much oxygen would make it's way down to the water if no mixing happens when put into container? I always hear of blanket of CO2 over a liquid. I'm trying to relearn some thermodynamics principles. Would the partial pressure between the CO2 never allow the oxygen diffuse into the water if...
  31. T

    Static Electricity vs Current in a Closed Circuit

    Hi, I'm an automotive technician. I have trouble understanding a couple basic electrical concepts. The problem is that I am more or less taught that current flows through CIRCUITs. When analyzing electrical problems, I think current will only flow if there is a voltage (potential...
  32. Spinnor

    Closed, collapsing universe+only photons at first -> matter when hot?

    Closed, collapsing universe+only photons at first --> matter when hot? Suppose we had closed, collapsing universe with a uniform thermal distribution of low energy photons like that of the CMB and no other matter (I suppose we must pick the initial conditions right for collapse to occur) . As...
  33. N

    Closed under addition and closed under scalar

    Could someone explain to me about what closed under addition and closed under scalar multiplication means? I have a patchy idea of what it is but how does it relates to A = {(x,y) | x^2 + y^2 <= 1}? What does A stands for? What does the language implies? Edit: My interpretation: Let's...
  34. 2

    Controlled systems - Closed loops

    1. Homework Statement [/b] http://snag.gy/m9Iq0.jpg Homework Equations The Attempt at a Solution I know that the sensistivity of a closed for at small change is given by the formula S = ∂ Ln T/∂ Ln G And T(s) = G_c(s)G(s)/1 + G_c(s)G(s) But since i don't have any G_c(s), i...
  35. M

    Is energy conserved in a closed system ?

    If I push a book horizontally across a table I do work. But is energy conserved?
  36. T

    A closed organ pipe has a length of 2.40 m?

    A closed organ pipe has a length of 2.40 m. a.) What is the frequency of the note played by the pipe? Use 343 m/s as the speed of sound. b.) When a second pipe is played at the same time, a 1.40 Hz beat note is heard. By how much is the second pipe too long? The a.) problem's solution is...
  37. E

    Why is the Triangle Set Not Closed?

    Homework Statement Homework Equations A set is closed if it contains alll of its boundary points. A boundary point is a point where an open ball around that point has one point inside the ball that's in the set, and one point in the ball that's not in the set.The Attempt at a Solution As seen...
  38. C

    Klein Gordon ret. Greens function on closed form

    In this note (http://sgovindarajan.wdfiles.com/local--files/serc2009/greenfunction.pdf) the Klein-Gordon retarded green function is derived on the form $$G_{ret}(x − x′) = \theta(t − t') \int \frac{d^3 \vec k}{(2\pi)^3 \omega_k} \sin \omega_k (t − t′) e^{i \vec{k}\cdot (\vec x - \vec x')}$$...
  39. A

    Exploring the "n+1" Sequence: Seeking a Closed Form Solution

    For a system I am studying the following sequence (which I would assume is quite common) came up: n1=1, n2=2, n3=4, n4=7, n5=11, n6=16, n7=22 ... i.e. the difference betweens two successive numbers grows with 1 as we move from (n_N-1, n_N) to (n_N,n_N+1). Is there a closed form expression f(k)...
  40. B

    MHB Showing a certain algebra is closed under inverses

    Let H be a hilbert space. Let T be a bounded normal operator on H. Consider the closure of the set of polynomials in $T$ and $T^{*}$. Show that if T has an inverse in B(H), then the inverse is in this generated algebra. Notes: This is pre-gelfand naimark so can't invoke that My thoughts: If...
  41. A

    Evaluating a Finite Sum to a Closed Form Expression

    I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.
  42. N

    Closed Feedback Loop mechanical system examples

    Homework Statement Hello everybody I was hoping some of you could give me some some examples of some closed feedback loop mechanical systems. This is for my controls class where we have to design our own control system. I'm having trouble trying figure out some systems. I know one would...
  43. B

    Sellafield partly closed after 'above normal' radiation

    http://www.bbc.co.uk/news/uk-england-cumbria-25975785 They have/had "above normal levels" at a perimeter detector. As far as I know this would detect airborne radiation. And presumably at far lower levels than the source. "A spokesman stressed there was no risk to the public or...
  44. 4

    What is the Minimum Depth of Water for Standing Sound Waves in a Drinking Glass?

    Homework Statement We place a speaker near the top of a drinking glass. The speaker emits sound waves with a frequency of 3.75 kHz. The glass is 14.1 cm deep. As I pour water into the glass, I find that at certain levels the sound is enhanced due to the excitation of standing sound waves in...
  45. K

    Liquid pressure in a closed system

    Homework Statement A steel cylinder filled with water contains 3000psi of pressure, completely sealed, walls ≈ infinite thick. No gas is present inside of the cylinder, and no heat exchange. To the problem; if a solid rod/piston enters on top of the cylinder with no possibilities to bleeding...
  46. K

    Stability of Closed Time-Like Curves: Current Status?

    I remember reading something, long ago, to the effect that any attempt at creating a CTC would be doomed by energy from vacuum fluctuations piling up through it and leading to explosive behavior (I think the idea originated in work done by Misner and Taub in 1969?). Does anyone know what is...
  47. J

    Integral symbol for closed loops over functions?

    I find it sometimes confusing dealing with integrals of multi-valued functions in distinguishing a closed integration path, and an integration path which forms a closed loop over the function. They can of course be quite different. For example: $$\oint f(z)dz.$$ Now, is the integration to...
  48. A

    Closed loop Servomechanism problem

    1. Homework Statement [/b] Hey Guys Firstly thanks for looking, I really appreciate any help or interest with my problem. The problem is a closed loop feedback system it's unlike any I have come across before. I have been given the definition which is as follows:- G(t)^-1 = 2.5...
  49. mathbalarka

    MHB Closed form chains of derivatives

    A recent post of chisigma rings me the bell of an old problem I thought of posting in a forum (either here or MMF). Is there any particular approach to computing a closed form for derivatives of certain smooth and continuous functions of $\mathbb{R}$? For example, it is easy to find the $n$-th...
  50. A

    What happens to an electron when its used in a closed circuit?

    Please help me to understand what happens to an electron when its used in a closed circuit. Main Question: How can electrons within a circuit perform work i.e. illuminate a light bulb or heat a stove and not be lost or changed from one state to another? How could it just stay the same and...
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