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. R

    Closed Orbit of Hydrogen Atoms. How to find the classical turning point

    Hi. I am trying to find the classical turning points in semi-parabolic coordinates for the hydrogen atom when an electric field is being applied to it in the y-axis. I am reading an article for those who are interested called Classical, semiclassical, and quantum dynamics in the lithium...
  2. X

    Building a Small Closed Wind Tunnel: Resources & Info

    Greetings, for the school I must find some information about the building of a small close wind tunnel . Some one know where to find it? Good day!
  3. D

    Closed set representation as union of closed intervals

    There the well known theorem that every open set (I'm talking about R here with standard topology) is the union of disjoint open intervals. Now, looking at the geometry, it seems that between any two adjacent open intervals which are in the union constituting our open set there is a closed...
  4. F

    What's the TeX for a double closed loop integral?

    Homework Statement I tried using \ooiint, I want a loop that circles both integrals (two), anyone know?
  5. K

    Q) A closed chamber containing working refrigerator is pefectly

    Q) A closed chamber containing working refrigerator is pefectly insulated and d door of refrigerator is opened, wat ll happen to temperature inside the chamber a)Decrease b) Remain same c) Increased d) Cant say coz it depends on quality of insulation
  6. Y

    Showing Range of Sequence in Metric Space is Not Always Closed

    Homework Statement show that (the range of) a sequence of points in a metric space is in general not a closed set. Show that it may be a closed set. 2. The attempt at a solution I don't know where to start. For example, if we are given a sequence of real numbers and the distance...
  7. Y

    Is the graph of f(x)=1/x a closed set?

    f(x)=1/x closed set?? A book I'm reading now says the graph of f(x)=1/x is a closed set, how come?? Its range is [(-\infty,0)\cup (0, \infty). A set is closed iff every convergent sequence has a limit point in the set. If a sequence converges to 0, then 0 is not in the range
  8. S

    Hi,i want to understand how fundamental group of a closed oriented

    Hi, i want to understand how fundamental group of a closed oriented 3-mfd determines all its homology and cohomology gorups. Please can you help me.
  9. Y

    Is X a Metric Space? Closed and Open Sets

    Assume X is a metric space, then X and the empty set are both closed and open, am I correct?
  10. T

    In a closed system does pressure vary with elevation?

    In a closed piping system (such as a chilled or hot water system in a tall building), is the water pressure at the top less than that at the bottom? Bernoulli's equation would lead you to believe that it is, but I cannot find anything explicitly stating that this applies to closed systems...
  11. H

    Find uncountably many subsets that are neither open nor closed

    Homework Statement 1. Find an uncountable number of subsets of metric spaces \left(\mathbb{R}^{n},d_{p}\right) and \left(\mathbb{C}^{n},d_{p}\right) that are neither open nor closed. 2. If 1\leq p<q , then the unit ball in \left(\mathbb{R}^{n},d_{p}\right) is contained in the unit ball in...
  12. jfy4

    A Closed Universe and the Horizon Problem

    Hi, one of the problems that inflation right after the Big Bang solves is the horizon problem. While this post is not really related to inflation, I was wondering why a closed universe is not a more favorable candidate for the solution to that problem, rather than inflation. Perhaps I...
  13. F

    Closed curves and Line Integrals

    Homework Statement Given \mathbf{F} = \nabla f\; where \;f(x,y) = sin(x-2y) Find a curve C that is not closed and satisfy the equation \int_C \mathbf{F}\cdot dr = 0The Attempt at a Solution \nabla f = \;<cos(x - 2y),-2cos(x-2y)> So to satisfy the dot product being 0 (I am hoping I can do...
  14. A

    Thermodynamics: Open or Closed System

    Ok this is solely for my interest. I should know this if I were taking Grade 12 Chemistry, but I haven't had this course in two years, and neither have I continued in pure science since then so please if you know better tell me if this is correct AND if it is only so because the case is of a...
  15. M

    Derivation of Fibonacci closed form

    See below
  16. I

    Closed disk of radius limit math problem

    Homework Statement If Dr is a closed disk of radius r centered at (a,b) find lim r->0 (1/pir2) \int\intfdA over Dr. The Attempt at a Solution From mean value equality, \int\int fdA = f(x,y)A(D) where A(D) is the area of the region which here is pir2. So the lhs becomes lim r->0 f(x,y)...
  17. R

    Closed loop vs open loop resistance magnet drop demo

    Hello everyone, curious about something here. I saw a demonstration lately were a magnet was dropped down a copper pipe and the magnet dropped very much slower than expected. What I got to thinking was, if you replaced the copper pipe with the same quantity of insulated copper wire in a...
  18. K

    Closed Form Solution | Definition & Meaning

    Hi Guys, What does the term Closed form solution mean?
  19. B

    Evaluate integral around a closed contour of f(z) dz f(z)=(sin z)/z

    Homework Statement evaluate integral around a closed contour (C) of f(z) dz, where C is the unit circle centred at the origin and f(z) is (sin z)/z Homework Equations The Attempt at a Solution well, the textbooks don't give a similar example
  20. B

    Union of Closed Sets: Finite vs. Infinite Examples

    A Union of a FINITE collection of closed sets is closed. But if it is an infinite collection? Can someone provide an example please?
  21. N

    PN-junctions: is the voltage measurable? Closed circuit?

    Hello, If I put a voltmeter over a (pn-junction) diode, do I measure anything? I would intuitively say "no". Is the following picture correct? So let's say the P-region is to the right, N-region to the left. If I were to attach a voltmeter across it, I'd have to attach a metal wire...
  22. Pengwuino

    Admissions UC Davis department admissions closed? (Anger enclosed)

    UC Davis department admissions closed?!? (Anger enclosed) So UC Davis dropped a damn bombshell on me this morning. I applied to the universities Department of Applied Science Graduate Program for the Fall 2011 semester. I get an e-mail this morning, MARCH 31ST, that I'm not even rejected, BUT...
  23. M

    Thermodynamics closed system - first law

    Homework Statement 1kg of water that is initially at 90 degrees celsius with a quality of 10% occupies a spring loaded piston cylinder device. The device is now heated until the pressure rises to 800kPa and the temperature is 250 degrees c Determine the total work done during this process...
  24. B

    Quadratic Forms: Closed Form from Values on Basis?

    Hi, Everyone: I have a quadratic form q, defined on Z<sup>4</sup> , and I know the value of q on each of the four basis vectors ( I know q is not linear, and there is a sort of "correction" for non-bilinearity between basis elements , whose values --on all pairs (a,b) of...
  25. E

    Discrete quotient group from closed subgroup

    Hi All, I've come across a theorem that I'm trying to prove, which states that: The quotient group G/H is a discrete group iff the normal subgroup H is open. In fact I'm only really interested in the direction H open implies G/H discrete.. To a lesser extent I'm also interested in the H...
  26. M

    Hilbert space question; show Y is complete iff closed

    I would like a second opinion on my answer to this question as I'm confusing myself thinking about my proof. Any input is appreciated Homework Statement "Let (X, ||.||) be a complete normed linear space and Y \subsetX be a non-empty subspace of X. Then (Y, ||.||) is a normed linear...
  27. M

    Hilbert space question; show Y is complete iff closed

    I would like a second opinion on my answer to this question as I'm confusing myself thinking about my proof. Any input is appreciated Homework Statement "Let (X, ||.||) be a complete normed linear space and Y \subsetX be a non-empty subspace of X. Then (Y, ||.||) is a normed linear space...
  28. H

    Closed systems and mass/energy transference

    So I am reading a text written by my Thermodinamics professor and I find something that I still can't accept. "(Sistema fechado) É aquele que não troca massa. (...) Um sistema fechado é dito isolado quando não troca energia. Entretanto, essa definição de sistema não é consistente com a teoria...
  29. E

    Closed Strings and Virasoro algebra

    Hey guys, i just started taking a course on ST and so far we discuss the closed string following Green, Schwarz, Witten. I don't see the point of constructing the Virasoro algebra (formula 2.1.85 in GSW) if the corresponding generators are zero due to the constraints. Or to put it differently...
  30. D

    Standing Wave in Closed Tubes Lab

    1. http://img856.imageshack.us/i/scanpic0001.png/ using tuning forks, you're supposed to choose 7 notes and find the frequency and length then find an approx speed for sound. we did this with logger pro and a USB microphone device and glass tubes. i plugged in my data to this eq'n: fn =...
  31. M

    Flow of electricity: Open versus Closed Circuit

    I need help understanding this conceptually, so can anybody please correct me and help me understand this? If I'm correct then just say so.Diagram: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/labVpic3.jpg the circles are bulbsOk so the basically in an open circuit there is no flow and...
  32. D

    Proper continuous map is closed

    Homework Statement Prove a proper continuous function from R to R is closed. Homework Equations proper functions have compact images corresponding to compact preimages, continuous functions have open images corresponding to open preimages, in R compact sets are closed and bounded...
  33. M

    Show that f is a closed subset

    Homework Statement (X,d) is a metric space B(x) is the set of all bounded functions on X show that f = {g \in B(X) g is continious} is a closed subsetThe Attempt at a Solution A hint of how to start?
  34. I

    Air flow rate in a closed pipe

    I can't seem to find an equation that fits the situation I am facing. Either that, or I just don't believe the answer the current equations are providing. I am trying to develop the size for an air compressor to fill up a train braking sytem. I have equations for most of the system, but I...
  35. B

    Understanding Closed Curves & Remark on Unique Extension

    I have a question about the Remark on the page posted. When it says "If γ and all its derivatives take the same value at a and b, there is a unique way to extend γ to a (b − a)-periodic (smooth) curve γ : R → R^n" what does this exactly mean? I suppose that the condition that the derivatives...
  36. W

    Wavelength of a wave in a closed tube

    Homework Statement In a lab that we performed, we had a closed tube with piezo electric transducers on both ends, and they were attached to a frequency generator. We found the frequencies that caused resonance, and the lab wants us to calculate the velocity of the wave using data. The lab...
  37. R

    Twist of an open versus closed cylinder

    Homework Statement a) Determine what the thickness should be in a closed tube versus an open tube to have the same twist angle b) Determine what the thickness should be in a closed tube versus an open tube to have the same max shear stress G=20GPa T=50Nm tr=1mm (for the open tube)...
  38. D

    Single positive electric charge in a closed universe

    Say, all objects in a closed Universe are neutral, and there is only 1 (unbalanced) positive charge. Lines of an electric field started on a positive charge can end only on the negative charge or they go into infinity. But in a closed universe there are no negative charges nor they can go...
  39. E

    Closed tube standing wave

    Standing waves have a fundamental frequency equal to 4x the length of the pipe if the pipe is closed at one end and open at the other end. So, blowing across the top of a 33.2 cm bottle should produce a fundamental frequency of v/4L or about 340/1.2= 283 hz. When I record the sound produced...
  40. M

    Real Analysis(open nor closed sets)

    Hello, I am having trouble finding an example of a set in R^2 that is neither open nor closed. I have already shown the half open interval [0,1) is neither open nor closed, but I can't seem to find any other examples. Can someone push me in the right direction? Would x^2+ y^2<1 be open nor...
  41. T

    Hypothetical questions with a closed system

    The 2nd law of thermodynamics refers to closed systems. 1. If we imagine a universe of infinite extent but where only one object exists that emits e/m waves, is that a closed system? 2. If we imagine a universe where only two asteroids exist and are orbiting each other, and a machine between...
  42. S

    Prove that the intersection of any collection of closed sets in a topological space X

    Prove that the intersection of any collection of closed sets in a topological space X is closed. Homework Statement Homework Equations The Attempt at a Solution
  43. T

    Topology - Use Componentwise Convergence Criterion to prove closed ball closed.

    Homework Statement Let r be a positive number and define F = {u in R^n | ||u|| <= r}. Use the Componentwise Convergence Criterion to prove F is closed.Homework Equations The Componentwise Convergence Criterion states: If {uk} in F converges to c, then pi(uk) converges to pi(c). That is, the...
  44. K

    Is accumulation point = adherent point in a closed set?

    A set S is closed iff it contains all its adherent points iff it contains all its accumulation point? From what I know, in general accumulation point is a subset of adherent point, but if supposed I have a closed set, then the "if and only if" forces me to conclude that accumulation point =...
  45. F

    Magnitude of a Net Charge within a closed surface

    Homework Statement A closed surface with dimensions a = b = 0.254 m and c = 0.4064 m is located as in the figure. The electric field throughout the region is nonuniform and given by ~E = (α + β x^2)ˆı where x is in meters, α = 4 N/C, and β = 6 N/(C m2). Picture of object attached...
  46. J

    Closed Loop Hot/Cold: Create Water From Air

    Im looking for a way to create solar heat activated condensation..Possibly a sodium acetate or zeolite/water system..A hot/Cold heat pump system generated only by heat and night time cooling to create a dehumidity effect..Basically create water from air with a chemical in a closed loop system.Is...
  47. Demon117

    Vector subspace F is closed in E

    Let E be the vector space of bounded functions f:N --> R, with the norm(g) = sup|f|. Assume without proof that the norm holds, so that the function d(f,g)=norm(f - g) is a metric. Prove that the vector subspace F={f in F | f(n) -->0 as n --> infinity} is closed in E. Here is what I have...
  48. S

    FRW metric for closed universe

    Hi, I'm new to Physics Forum and wasn't really sure where to post this since its not strictly speaking a homwork question. So if it happens to be in the wrong place I apologise. I was looking through some lecture notes from when I did my Physics degree years ago and come across a problem...
  49. I

    Matrix representation of a closed symmetric operator

    Homework Statement Show that a closed symmetric operator has a matrix representation. Homework Equations There are lots. I'm hoping somebody familiar with linear operators in Hilbert spaces is reading this! The Attempt at a Solution Hi, I'm trying to prove that a closed...
  50. V

    Set closed in Y, but not in superset of Y, X?

    Homework Statement Let Y be a subset of X. Give an example where a set A is closed in Y but not closed in X. Homework Equations A set is closed if its complement is open. A set is open if for every element x0 of the set, there exists an E > 0 such that U(x0;E) = {x|d(x,x0)< E} is...
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