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.

View More On Wikipedia.org
Recent contents Top users
  1. T

    Why do plastic containers deform in hot temperatures?

    I have a plastic Gatorade type bottle that I reuse. Between uses, I fill it with hot water and shake, and then empty it. Once I empty it, if I put the lid on and wait, the bottle eventually deforms and sucks in on itself. Then when I remove the lid it returns to normal. Why does it deform? Is...
  2. G

    Are closed time like curves an inherent feature of rotating universe models?

    This is a follow up to my previous question, as they appear that in both the Godel Metric and the Van Stockum dust Perhaps a better way to put this is, could there be a model where you had rotation (maybe around a non-symmetrical axis?) and not get these CTCs?
  3. Y

    Thermodynamics - Double U Tube Manometer with 2 Closed Ends

    Thermodynamics -- Double U Tube Manometer with 2 Closed Ends Homework Statement GIVEN: Fresh water and sea water in parallel horizontal pipelines are connected to each other by a double U tube manometer. Density of sea water is 1035 kg/m^3 Density of air is 1.2 kg/m^3 Standard temp and...
  4. qspeechc

    Absolutely Closed Metric Spaces.

    Hi. An absolutely closed metric space M is such that: If N is a meric space containing M, then M is closed in N. I would like to show that an absolutely closed metric space is complete, how do I do this? I know the proof of the converse but that's no help obviously. I know intuitively...
  5. R

    Closed tank and inverted manometer question

    Hey guy this is my first post here. I am looking for a little bit of help with a past paper I've been looking over. I've had a look at it and I am drawing a blank due to being off ill when this was covered in class, if anyone would be so kind as to show me how to get started on this question I...
  6. N

    Calculating pressure in 2-phase closed systems

    I have a closed pressure vessel that is partially filled with water and the head space has been purged with He and charged to about 100 psi. What I wish to know is how to calculate the overall pressure in this vessel after heating it to a given temperature (e.g., 300 or 400 C). I know the...
  7. R

    Closed loop induction Study?

    Searching on the net for "closed loop induction" refers mostly to motors. What terms would I use to find information on the dynamics, if I can call it that, the B field that is the out-come of an induced current in this closed loop coil? I would think that the coils architecture would produce...
  8. E

    Stoke's Theorem around a closed circle

    Homework Statement What is the line Integral of the function f = yi-xj+zk (where i,j,k, are cartesian unit vectors) around a circle with radius R centered at the origin? Homework Equations Stokes Theorem: i.e. the integreal of some function between a and b is equal to the difference in...
  9. O

    Double integral bounded by closed parametric curve

    question: how do i find the area under f[x,y] bounded by a closed parametric curve x[t],y[t]? it doesn't look like i can use a change of variables. it seems as though double integrals only with functions where the curve is given explicitly such as y[x] or x[y].
  10. I

    Calculating pipe size for closed loop watering system

    I am building a closed loop watering system and need help determining the minimum size pipe I need for the return drain pipe. The system will pump water from a reservoir through spray nozzles into 4 containers at a rate of 300 gallons per hour. Each container will have a drain pipe in the bottom...
  11. G

    Understanding How Closed Curves Work in Maths

    Hey, I am wondering if anyone can help me understand a mathematical explanation as to how they work. From what I understand, the area under a closed curve is the same, independent of the path taken. So when doing an integral you only need to take the initial and final into account. There have...
  12. J

    Heated water in closed cylinder with electricity

    Hey, I guess I came to right sub-topic, since I knew here I may have not noticed every thing.. One sleepless night I was thinking about what would happen IF: in a closed isolated cylinder would be alomost full of H20(+some salt if required). anode and catode in sides, so what electricity...
  13. Q

    Calculating Resonant Frequencies of Closed Air Columns

    Homework Statement A closed air column is 60.0cm long. Calculate the frequency of the forks that will cause resonance at: a) the first resonant length b) the second resonant length Note that the speed of sound is 344m/s. Homework Equations Ln = (2n - 1) * \lambda / 4 fn =...
  14. Q

    Where has the energy of the closed photon packet gone?

    A photon is emitted from a star in a far away galaxy. Its energy is hv = 1000 keV Its velocity is c. When it arrives at the retina, the redshift/doppler caused the photon to have an energy less than 1000keV. Where has the energy of the closed photon packet gone?
  15. H

    Seeking the Shortest Closed Curve in a Homology Class

    I am seeking the answer to the following question: Given a simple closed curve on a compact Riemannian surface(a compact surface with a Riemannian metric), whether there exists, in the homology class of this simple closed curve, a (single) closed curve which has the shortest length measured with...
  16. Z

    Calculating Length of Closed Orbits: Gutzwiller Formula & Hamiltonian Systems"

    given a Hamiltonian H=p^2 + V(x) how can you calculate the length of the closed orbits ? , i mean in gutzwiller formula you must perform a summation over the length of the closed orbits to calculate density of states g(E) but how can you know what the lenghts are ?? .. of course for Harmonic...
  17. S

    Gain Margin, Open or Closed Loop?

    Homework Statement I'm given a closed loop transfer function with a gain, K=1 and a plant H(s). I need to find the gain margin of the system. Homework Equations I know how to solve this problem: a) I find the frequency where the phase is -180 degrees. b) I find the gain at that...
  18. L

    Gravity violating the conservation of energy in a closed system?

    I have devised a simple thought experiment which leads me to an absurd conclusion and I feel I’m missing something obvious but I can't see where I’m wrong and I hope you could help point out my error. I start with an empty space initially containing two masses that are at rest relative to...
  19. L

    Closed sets in a topological space

    If A\subseteq B are both subsets of a topological space (X,\tau), is it true that any closed subset of A is also a closed subset of B?
  20. J

    Exploring CTCs: Can Objects Travel Through Time?

    im trying to understand the theory of this. is a CTC supposed to actually bring an object back to the original time? or is it supposed to make it appear that way to an outside observer? I am reading up on it from wikipedia: http://en.wikipedia.org/wiki/Closed_timelike_curve but in the beginning...
  21. S

    The Hawking 4D closed manifold

    Hi, I am struggling to understand Stephen Hawking's view of the universe as a 4D closed manifold. In a recent interview, I believe he had this to say: What I don't understand is how this theory is compatible with the scientific observation that the universe is expanding? I have 2 questions: 1)...
  22. T

    Calculating Volume of a Closed Cylinder with 600π Surface Area

    Homework Statement A closed cylinder has total surface area equal to 600\pi . Show that the volume, Vcm3, of this cylinder is given by the formula v = 300\pi-\pi r^3 , where r cm is the radius of the cylinder. Find the maximum volume of such a cylinder. Homework Equations...
  23. C

    Find closed form of series SUM (nx)^(2n)

    If abs x < 1 find a closed form function (i.e. f(x) = x +1) for the following series: \sum((nx)^(2n)) (reads: the series from n=1 to infinity of nx^(2n))
  24. C

    Electric potential in a closed loop wire

    Homework Statement A closed loop of wire that has uniform linear density lambda is bent into the shape shown below, with dimension as indicated. Find the electric potential at point O, assuming it is zero at infinity. (see the attachment)Homework Equations V = k q /r The Attempt at a...
  25. V

    Double slit experiment (one slit closed)

    Hi, In young experiment, say one slit is completely closed, what observed is looks like a single band light. But why is not a diffraction pattern? I wonder whether the reason is, the slit width(don't mean distance between slits) more narrow than single slit diffraction in Young experiment?
  26. V

    Fundamental Frequency of Open and Closed Tube

    Homework Statement A tube closed at one end and open at the other has a fundamental frequency of 242 Hz. What is the fundamental whenboth are open? Homework Equations f (open and closed) = v/4L f (open) = v/2L v sound = 343 m/s The Attempt at a Solution f1 (open and closed) =...
  27. M

    Metric spaces and closed balls

    Homework Statement Can anyone suggest a simple example of a metric space which has a closed ball of radius, say, 1.001 which contains 100 disjoint closed balls of radius one? I've taught myself about metric spaces recently so I'm only just getting started on it really, not really sure how...
  28. P

    Closure of f(A): Is it a Closed Set?

    Given that f is a function from R(=real Nos) to R continuous on R AND ,A any subset of R,IS THE closure of f(A) ,a closed set??
  29. W

    Sound of Music - Closed Organ Pipe

    1. One closed organ pipe has a length of 2.40m. a. What is the frequency of the note played by this pipe? 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? 2. f = nv/2L (n = 1) change...
  30. A

    Finding Closed Surfaces for Point Charge at Origin

    If there's a point charge at the origin, I want to find two closed surfaces such that the flux through one of them is zero while the other is not. I know this may seem trivial but I just want to make sure I understand the question. My answer would be that to get a zero flux, the closed...
  31. L

    Is this true about the emf in a closed circular wire?

    the emf is defined as the potential difference between two points \varphi(\vec{r_1})-\varphi(\vec{r_2}). ok so let's say we make a trip round a closed circular wire with a battery to keep the current flowing then r1=r2 and so no emf has been done - is this true and if so why?
  32. K

    Coming up with recursive and closed form expressions

    Homework Statement I am having some trouble coming up with recursive and closed form expressions of different sequences. I realize helping me with this would pretty much just be giving me the answer, but if anyone could also help me with how to think of the answers that would be nice. 1) Cn =...
  33. M

    Show Co is Closed in L∞: Finding Ko

    I want to show the Banach space co is closed in l∞ . So, I pick a convergent sequence x_n in co that converges to x in l∞ Now, x_n --> x: given e>0, there is an N_e s.t. for all n>N_e, ||x_n -x ||= Sup |x_n(k)-x(k)|<e (we're supping over k). Since x_n is a sequence in co , for each...
  34. E

    Escape from totally closed empty room

    Hi guys! I have one question that bothers me for reeeeally long time (and it's NOT homework! :-) I found one question which goes like this "How can physics help you escape from a totally closed empty room?" Of course it means that room doesn't have any doors or windows, it would be too easy to...
  35. G

    What is the smallest closed subset of Z containing 2 and 0?

    The question given is: Determine the smallest subset A of Z such that 2 ε A and A is closed with respect to addition. The answer given was the set of all positive even integers, but I was thinking that the smallest subset would be the given element and the identity element (0 in this case) so...
  36. T

    Closed non-commutative operation on N

    Homework Statement (i) Give an example of a closed non-commutative binary operation on N (the set of all natural numbers). (ii) Give an example of a closed non-associative binary operation on N. The attempt at a solution This has me stumped, there must be something simple that I'm missing. I...
  37. Spinnor

    Force between two charges in closed universe

    Say we have two charges in a closed spherical universe, of radius R, a distance r apart. If the charges are close, r<<R, we might guess that the force would go as 1/r^2? Let the two charges move away from each other till they are as far apart as possible. At this point the force between...
  38. M

    Proving the Closedness of a Linear Subspace in a Normed Space Using Dual Spaces

    Let X be a normed space, F be a closed linear subspace of X, Let z be in X, z is not in F. Let S={x+az:a is in the field Phi}=Span of F and z We show S is closed. I would define a function f : S--> Phi by f(x+az)=a and show that |f|< or equal to 1/d where d= distance(z,F) hence f is in...
  39. F

    Resonance in Closed air columns

    is is based on the experiment where we had to find the point in which tuning fork forces air inside open-ended air column into resonance, the length of the tube is altered by changing the water level in the tube. the water level can be altered by raising or lowering a reservoir of water, thus...
  40. B

    Vector spaces, closed under addition

    Homework Statement Let S={A (element) M2(R) : det(A) = 0} (b) Give an explicit example illustrating that S is not closed under matrix addition.Homework Equations The Attempt at a Solution 1) I think that the problem is saying S is a set of 2x2 matrices, whose determinant is zero? 2) I'm...
  41. A

    Gamma Function in closed form?

    Could you consider the gamma function to be a closed form representation? If I could express a numerical series in terms of the gamma function, would it be considered a closed form representation?
  42. A

    Is there a closed form for the harmonic series?

    Taking from Euler's offering that: \Sigma1/n= ln(n) + \gamma could you say that there is a closed form of the harmonic series? Does Euler's offering qualify?
  43. A

    Evaluate an Infinite Series in Closed Form

    My question is one of vocabulary. What does it mean to evaluate an infinite series in closed form? If I have a Series: \Sigma 1/ (N2), as N goes from 1 to infinity. This is similar to a test question I'm working on so, I DO NOT want to know how to solve it, I just want to know exactly...
  44. C

    Year 12 Sound Problem (Involves resonance in a closed pipe).

    Homework Statement Hi :) This question is from a test i had today. For some stupid reason we get to finish it off tomorrow. I figured i do what everyone else will, and sort out the what i didn't understand. Luckily this was it. Anyway, the question is typed from memory so it may seem a bit odd...
  45. MTd2

    How does an electron behave in a closed time like curve?

    So, it goes in the first loop, no problem. In the second loop, no problem either, it could just change the spin. So, what about the third, will the electron interfere with its own past? Will it be destroyed? Will it mysteriously scatter and not interfere with its past. This is the same for all...
  46. I

    Identifying three identical metal bars (with your eyes closed )

    Identifying three identical metal bars (with your eyes closed!) Homework Statement How would you determine, non-destructively, and with eyes closed, which is which amongst three identically-shaped metal bars known to consist of a permanent magnet, a piece of soft iron and a piece of copper...
  47. D

    Can the Universe have a positive curvature everywhere and still be infinite?

    I wonder if Universe with a positive curvature everywhere can be infinite. As an example I see a spring: you make a full rotation, but you don't get into the same place, but another place. Spring is 1-dimensional object (line) so curvature is not defined for it. But is it possible for the...
  48. S

    How can a metrix space be open and closed?

    Homework Statement How can a metrix space be open and closed?
  49. Demystifier

    How do D-branes fit into closed string theories?

    By definition, D(irichle)-branes are branes on which open strings end. Then how closed string theories IIA and IIB may contain D-branes? Or more precisely, why the branes appearing in closed string theories are still called D-branes?
  50. A

    Is the Translation of Open and Closed Sets in R^n Also Open or Closed?

    Homework Statement Let A be a subset of Rn and let \vec{w} be a point in Rn. Show that A is open if and only if A + \vec{w} is open. Show that A is closed if and only if A + \vec{w} is closed. Homework Equations The translate of A by \vec{w} is defined by A + \vec{w} := {\vec{w} +...
Back
Top