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. E

    Show that the set S is Closed but not Compact

    Homework Statement Show that the set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2 is closed but not compact. Homework Equations set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2 The Attempt at a Solution I set x = 0 and then y = 0 giving me [0,±√3] and [±√3,0] which means it is closed However, for it to...
  2. E

    Are the following Sets: Open, Closed, Compact, Connected

    Homework Statement Ok I created this question to check my thinking. Are the following Sets: Open, Closed, Compact, Connected Note: Apologies for bad notation. S: [0,1)∪(1,2] V: [0,1)∩(1,2] Homework Equations S: [0,1)∪(1,2] V: [0,1)∩(1,2] The Attempt at a Solution S: [0,1)∪(1,2] Closed -...
  3. V

    Is it practically possible to construct a closed system?

    In practice, is a closed or isolated system possible? My friends keep saying No, but isn't a system inside say, a vacuum isolated? There is no outer atmosphere for transfer of energy to take place.
  4. M

    Determine whether set is closed, open or neither.

    Homework Statement D1 = {(x,y) : x^2 + y^2 < 3, x+2y = 2} D2={(x,y) : x^2 + y^2 > 2} D3={(x,y) : x + 2y = 2} Homework EquationsThe Attempt at a Solution D1 is neither, D2 is open and D3 is closed, am I right or wrong?
  5. nomadreid

    Does an operation have to be closed?

    According to both Wikipedia and Wolfram MathWorld, a binary operation must be closed. Wiki does leave room for a so-called external binary operation, i.e. a function from (K X S) to S, but not from (S X S) to K. (This would make the operators in physics actually "external operators", no? Do we...
  6. Heisenberg1993

    Event Horizon in a closed, matter (dust) dominated universe

    Hi! It is stated in V. Mukhanov's book "Physical foundations of Cosmology" the following (page 44, after equation 2.25): "In contrast, for the dust dominated universe, where ηmax=2π, the event horizon exists only during the contraction phase when η>π." could someone please explain why is this...
  7. B

    Differentiability in an open and closed intervals

    Is there an f(x) which is differentiable n times in a closed interval and (n+1) times in an open interval? I think I saw this in a paper related to Taylor's theorem (could be something else though). It didn't make sense to me, how can something be differentiable more in an interval that contains...
  8. J

    Engineering I thought circuits had to be closed

    Homework Statement I am supposed to determine the potential differences between the points. However, I thought circuits had to be closed...
  9. T

    Biot-Savart non-textbook Equation -- B at point above a loop but off-axis

    I read everywhere about the formulas for calculating B at a point from a length of straight wire, or at a point from the centre of a closed loop. But what about at a point over a closed loop that wasn't the centre? Is there a simple calculation for that? Thanks
  10. F

    Intersection of a closed convex set

    Let X be a real Banach Space, C be a closed convex subset of X. Define Lc = {f: f - a ∈ X* for some real number a and f(x) ≥ 0 for all x ∈ C} (X* is the dual space of X) Using a version of the Hahn - Banach Theorem to show that C = ∩ {x ∈ X: f(x) ≥ 0} with the index f ∈ Lc under the...
  11. N

    Time Travel to the Past: CTC or Wormhole?

    In theory, is time travel to the past possible by traveling completely around the loop of the CTC (where it would seem future links with its own past) or is a wormhole the only way to time travel by way of short cutting the CTC.
  12. A

    Sound wave inside a closed cylinder - Bessel function

    Homework Statement The question is as follows, there is a cylinder with length L and radius R, there is a sound wave with a phase velocity v, they ask for the normal modes and the 5 lowest frequencies when L=R Homework Equations Wave equation for 3D, (d^2/dt^2)ψ=v^2*(∇^2)ψ The Attempt at a...
  13. P

    Sound waves in a closed pipe Problem

    Homework Statement Before I write the question you should know that my maths is all correct in my solution but I must have used the formulas incorrectly (or used the wrong formulas). I can't pinpoint where I've gone wrong or if I have left a formula out (I'm a teacher solving this question for...
  14. A

    Proof using the closed graph theorem

    Hi, I'm stuck on a problem in functional analysis. Let x be a sequence on the Natural nummers such that for any square summable sequence y, the product sequence xy is absolutely summable. Then x is square summable. Hint : Use the Closed graph theorem. If I can prove the map Tx : y -> xy had a...
  15. W

    Engineering Tough Circuit Problem, Find Current When Switch is Closed

    Homework Statement I got questions a) and b), but I'm stuck at c) and d). Homework Equations Kirchhoff's Loop and Junction rules. Equivalent resistance in series: Req = R1 + R2 Equivalent resistance in parallel: Req = ((R1)-1 + (R2)-1)-1 The Attempt at a Solution I really haven't gotten...
  16. diracdelta

    Find Length of Closed Pipe for Equal Frequency

    Homework Statement Open and closed pipe, give 5 beats per second. Open pipe is 30 cm long and gives a tone of frequency f0. Speed of sound is 330 m/s. How long do we need to extend closed pipe so both pipes give equal frequencies? Homework Equations Open pipe, fn=n*f1, f1=v/(2L) Closed...
  17. R

    Pressure caused by explosion in closed container

    Homework Statement (C2H4NO6, EGDN) is an explosive with perfect attributes. We fill 20% of a sealed container with an EGDN. Assume that EGDN explodes and the created gas bahaves according to ideal gas law. What is the excess pressure in the sealed container? My problem: I don't know where to...
  18. B

    Volume flow through a one side closed capillary

    Hi everyone, I'm doing a simulation and need some help. A capillary which is closed on both ends with the length l (x=0 to x=l), with a radius R and the volume pi*R^2*l is dropped on a parachut at the time t=0 from a hight h above ground. At t=0 the pressure inside the capillary is p_i0 (this...
  19. gauss44

    Coffee cup, bomb calorimeter: Open, closed, or isolated?

    Is a coffee cup usually considered to be a closed system? Why or why not? Does it matter that steam or hot coffee may be evaporating? (I think the steam is usually considered to be an insignificant amount of matter, allowing classification to be a closed system, but am unsure.) Is a bomb...
  20. gracy

    Closed Packing: Definition & Planes

    what is definition of closed packing?a close packing plane is a plane that the atoms cannot be packed any closer?
  21. A

    Determining if a pipe is open or closed from given the resonant frequencies

    Homework Statement A pipe resonates at successive frequencies of 540 Hz, 450 Hz, and 350Hz. Is this an open or a closed pipe? Homework Equations -- The Attempt at a Solution My assumption is that because the harmonics of an open pipe are odd number multiples of the fundamental frequency (1f...
  22. gracy

    Vapor Pressure: Closed-Systems Only? Open or Closed?

    Vapor pressure possible only in closed system? b.p is when vapor pressure become equal to atmospheric pressure in which system closed or open ?
  23. R

    What is a closed pipe ( standing waves)

    Homework Statement does it mean only one side of the pipe is open or both sides are closed. Homework EquationsThe Attempt at a Solution i think it means only one side is open, but i just need to make sure
  24. Breo

    Closed and Exact Forms on 2-Torus: Solving for Global Definitions and Exactness

    Homework Statement Now consider a 2-torus ## S_1 × S_1## and a coordinate patch with coordinates ## (\alpha_1, \alpha_2)## such that ## 0 < \alpha_i < 2 \pi##. Let us introduce in this patch a 1-form of the type: $$\omega = (A + B\alpha_2 + C sin(\alpha_2 ) + D cos(2\alpha_1 + \alpha_2...
  25. O

    Understanding the Closed Mobius Strip: Get Help Here!

    Why Mobius strip closed?Mobius strip is compact because it is confined and closed. But I can't understand closed of Mobius strip. Help please.
  26. 2

    [CalcII/DiffEq] Closed form expression for f(x) which the series converges

    Homework Statement Find a closed form expression for the function f(x) which the power series Σn=0..∞ n(-1)nxn+1 converges to and determine the values of x for which f(x) equals the given power series. Homework Equations N/A The Attempt at a Solution I'm actually not sure how to start. First...
  27. S

    Electromagnetic field profile around a closed loop

    Is there a way to determine the profile of the field around a charged closed loop - particularly on the direction normal to the plane of the loop, both front and back? For generic values of V, I, B, H, etc., and any dimensions of the loop, any particular formulae possible to obtain? Thank you...
  28. STEMucator

    LaTeX Closed Integrals in LaTeX: Forum Q&A

    Does the forum have built in LaTeX for multiple closed integrals? I know that ##\oint## is for a single contour integral. I would've expected things like \oiint and \oiiint to work for surface and volume integrals.
  29. V

    Behavior of gaseous oxygen in a closed box under magnetic field?

    Hi all, I'm new here, and I hope I'm doing this right. I mean posting where I should. Feel free to let me know. ;-) First, I'm a biologist but I'm a scientist and I'm interested in magnets recently. I read that magnetic field attract oxygen liquid (all over you tube) and also gaseous since...
  30. J

    Closed Loop Contour: Finding Threshold W Values

    I have a multivariable function, z = f(x, y, w), represented by a surface plot in 3D (z versus xy) for each value of w. As w varies, the function z varies (goes up and down and changes shape) over a given rectangular xy region. As z varies with w, contour lines with given constant values of z...
  31. J

    Closed Form Equations for Elasticity Properties for Anisotropic Materials

    Hi all, I'm wondering if anyone knows of a way to obtain elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from the terms of a 6x6 anisotropic stiffness or compliance matrix. I'm looking for a closed form solution, preferably. I would think that there should be a closed form...
  32. Z

    Open loop vs Closed loop Transfer Functions

    Okay, I have a simple plant which is 1/s*(s+1) Two poles on 0 and -1 and no zeros. This is the case for open loop. But when I close the loop with unity feedback and add a K gain, I end up with following transfer function; K/s^2 + s + K So, clearly the poles are now at somewhere else. However...
  33. R

    MHB What is a Closed Chain in Transportation Problem Solving?

    What is a closed chain (or circuit) that is used in solving a transportation problem (a special type of linear programming problem)? I'm having some problems with it. Please clarify it. I read its definition in a book, but it was not clear. I searched the net, but I failed in finding a...
  34. M

    Finding the Normal Cone of a Closed Convex Subset in a Hilbert Space

    Let \text{ } H \text{ }be \text{ }a \text{ } Hilbert \text{ } space, \text{ }K \text{ }be \text{ }a \text{ }closed\text{ }convex\text{ }subset \text{ } of \text{ }H \text{ }and \text{ }x_{0}\in K. \text{ }Then \\N_{K}(x_{0}) =\{y\in K:\langle y,x-x_{0}\rangle \leq 0,\forall x\in K\} .\text{...
  35. M

    MHB Why Is a Rectangle Considered Closed and Bounded in Volume Proofs?

    Hey! :o I am looking at the proof of the theorem that for any rectangle the outer measure is equal to the volume. At the beginning of the proof there is the following sentence: It is enough to look at the case where the rectangle R is closed and bounded. Why does it stand?? (Wondering) Is...
  36. W

    Complements of Curves in Closed Surfaces: Homeomorphic?

    Hi, let ## \alpha, \gamma ## be non-isotopic curves in a compact, oriented surface S. There is a result to the effect that ## S-\alpha## is homeo. to ## S- \gamma ## . This is not true as stated; we can , e.g., remove a disk (trivial class) in a copy of S and then remove a meridian ( a...
  37. S

    Zero Electric Flux Through a Closed Surface

    I'm relearning basic electricity concepts and I can't find an answer to a situation I've thought up. Imagine a cube with no enclosed charge and an electric field through it parallel to two of its faces. Guass's law says that the flux should be zero because there is no enclosed charge. Every...
  38. S

    Question on zero electric flux through a closed surface.

    I'm relearning basic electricity concepts and I can't find an answer to a situation I've thought up. Imagine a cube with no enclosed charge and an electric field through it parallel to two of its faces. Guass's law says that the flux should be zero because there is no enclosed charge. Every...
  39. stevendaryl

    Infinite Sum of Powers: Is There a Closed Form for the Series?

    This isn't quite a calculus question, but it didn't seem right for any of the other mathematics forums, either. Does anybody if there is a closed form for the following infinite series: \sum_n x^{n^2} for 0 < x < 1
  40. maverick280857

    Boundary conditions for open and closed strings

    Hi, I am a bit confused about the terminology used for the boundary conditions describing open and closed strings. For the open string, Ramond case: \psi^+(\sigma = \pi, t) = \psi^-(\sigma = \pi, t) Neveu-Schwarz case: \psi^+(\sigma = \pi, t) = -\psi^-(\sigma = \pi, t) Question 1: Is it...
  41. W

    Why only Closed Forms Matter in DeRham Cohomology?

    Hi All, One gets homological/topological information (DeRham cohomology ) from a manifold by forming the algebraic quotients H^Dr (n):= (Closed n-Forms)/(Exact n- Forms) Why do we care only about closed forms ? I imagine we can use DeRham's theorem that gives us a specific...
  42. F

    Find heat loss given metabolic rate in a closed system

    Homework Statement A 60 kg person is exercising in the gym, doing external work at a rate of 200W. If they have an efficiency of 20%, calculate the rate of temperature increase of their body if none of this heat was able to be transferred to their surrounds. (a) 828 ◦C per hour. (b) 13.8 ◦C...
  43. m4r35n357

    Can Einstein's Equations be Applied to a Closed Universe?

    I've been starting to look at the Hilbert action derivation of Einstein's equations, and have an introductory question. When the Lagrangian is excpanded into three integrals (for variation of metric determinant, metric and Ricci Tensor), the Ricci term is always dropped after a discussion of...
  44. M

    Wave reflection in Closed End Wind Instrument

    Hi, I am a little confused with the phase change that occurs in closed end wind instruments. According to http://newt.phys.unsw.edu.au/jw/flutes.v.clarinets.html, the phase does not change when the sound wave reflects off the closed end of the instrument. I thought that the phase changes by 180...
  45. P

    Thermomystery -entropy generation in a closed system

    My question relates to entropy generation in a closed system ΔS=dQrev/T for a reversible process ΔS=dQ/T + Sgen for an irreversible process This seems to suggest that Sgen arises because of the irreversibility of the heat transfer process (eg across a finite temperature difference). If...
  46. Soumalya

    Exergy Analysis of a Closed System

    I was going through "Engineering Thermodynamics" by Cengel & Boles studying exergy analysis of a closed(non flow) system.Referring to the attachment as you can see the equation, δWHE=δQ(1-T0/T)=δQ-T0/T.δQ should give δQ=δWHE+T0dS (using dS=δQ/T) but in the textbook...
  47. johann1301

    Is the Set N Closed for Addition in English?

    If you take two arbitrary numbers from a set N - let's say N stands for the natural numbers - and add them together, the sum will always be an element of N. In my language, there is a word for this, but i don't know what it is in english? If i translate it from norwegian, it would be something...
  48. B

    Open And Closed Discs - What's The Difference?

    Hello, i'm working through Lang's 'Introduction To Linear Algebra' and am on page 18 (in case any of you are familiar with it). He says that the set of points X, such that ||X - P|| < a where P is a point in the plane and a is a number > 0 is an open disc. He then goes on to say that ||X -...
  49. Greg Bernhardt

    What are closed timelike curves

    Definition/Summary In mathematical physics, a closed timelike curve (CTC) is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point. 'Inside the inner horizon (of a charged/rotating black hole) there is a toroidal region...
  50. 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...
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