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. Nathanael

    Closed trajectory in a central field of force; find the mass

    Homework Statement A particle moves along a closed trajectory in a central field of force where the particle's potential energy is U=kr2 (k is a positive constant, r is the distance of the particle from the center O of the field). Find the mass of the particle if it's minimum distance from O...
  2. moenste

    Find fundamental freq. and 1st overtone closed each end pipe

    Homework Statement Calculate the frequency of: (a) the fundamental, (b) the first overtone, produced by a pipe of length 40 cm which is closed at each end. (Velocity of sound in air = 340 m s-1.) Answers: (a) 425 Hz, (b) 850 Hz 2. The attempt at a solution L = 0.4 m, v = 340 m s-1 (a) f1 = ...
  3. H

    Closed Analytic Form of exp(ξG): Solved!

    what is the closed analytical form of exp(ξG) ? could you help me !
  4. gfd43tg

    What are the Closed Loop Transfer Function Parameters for a PI Controller?

    Homework Statement Homework EquationsThe Attempt at a Solution I don't think you need to see the problem to figure this one out, if needed I will post it (takes up a lot of space in the thread). I know for a PI controller, the controller transfer function is given $$ g_{c} = k_{c} \frac...
  5. jdawg

    Energy Balance for closed rigid container

    Homework Statement Water, initially saturated vapor at 4 bar, fills a closed, rigid container, The water is heated until its temperature is 400C. For the water, determine the heat transfer in KJ per kg of water . Homework EquationsThe Attempt at a Solution Assume potential and kinetic...
  6. shanepitts

    Are Finite Families of Closed Sets Closed?

    Homework Statement Let {Ei: 1≤i≤n} be a finite family of closed sets. Then ∪i=1n Ei is closed. Homework Equations Noting that (Ei)c is open The Attempt at a Solution Honestly, I have no idea where to start. I tried to demonstrate that Eai≥Ei if a is a constant greater than zero. Then...
  7. evinda

    MHB Understanding Open/Closed Sets in $\mathbb{R}^n$

    Hello! (Wave) The following definition is given: A set $U \subset \mathbb{R}^n$ is called open if for each $x \in U$ there is $B_d(x, \epsilon) := \{ y \in \mathbb{R}^n: d(x,y)< \epsilon\}$ -> open ball with center $x$ and radius $\epsilon$. Could you explain me why the following set is open...
  8. N

    I Closed Timelike Curves Explained in Layman's Terms

    Would someone explain to me in lay men's terms exactly what a CTC is. I understand that it is a closed timeline curve and that it allows( in theory) time travel to one's past. My question is how does one get into a CTC: Do you have to be traveling in space and at a certain speed? Does one...
  9. S

    Pressure exerted by a fluid in a closed container

    When a hole is made in the side of the container holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, what will happen to the water flow? I think that the water flow will follow a similar trajectory..what effect can gravity have on it? it...
  10. I

    Decrease in temperature and pressure of closed container

    Homework Statement Helium is stored in a tank initially at temperature To and pressure Po. It starts coming out through an opening (pipe outlet) at a constant mass flow rate of mdot. Calculate the decrease in temperature and pressure of the tank (assuming no heat loss to the surroundings) as a...
  11. yango_17

    Determining whether a set is open, closed, or neither

    Homework Statement Determine whether the given set is open or closed (or neither): {(x,y,z) ε R^3, 1<x^2+y^2<4} Homework EquationsThe Attempt at a Solution I believe that the set is open due to the only bounds being inequalities that are less than, not less than or equal to, but that seems...
  12. Ahmad Kishki

    Closed Set Proof: Show Limit Points of A is Closed

    Homework Statement Show that the set of limit points of the set ##A \subseteq \mathbb{R}## given by ##L## is a closed set.2. Relevant theorems Definition: A closed set F (subset of R) is such that it contains its limit points. Definition: A limit point x of a set A (subset of R) is such that...
  13. D

    Exploring Closed Systems & External Forces

    Homework Statement apparently momentum is only sure to be conserved in a closed system - no external forces. So that means if a toy car collides with a wall then the total momentum efter won't be the same as before. That is because the wall would be joined to something else and ultimately to...
  14. L

    First law of thermodynamics applied to a closed system

    Homework Statement - A well insulated rigid steel tank contains water (only) - A resistance heating element (240V, 3.67Amp) designed to heat the water as well as inlet and outlet valves for - the water. - At state-1, the water is in a saturated liquid-vapor mixture state at P(abs)=100kPa...
  15. RyanH42

    Closed system Energy transformation

    Lets suppose we have a close system.In this system we have a particles.The total mass of particles is M. The total energy of system will be ##E_x+E_M=E_t## (I made the system like this) Here ##E_x## is just energy,its not important.##E_m## is the energy of masses.Now I want to move this...
  16. Master replies:

    Is the closed string an unknot?

    A unknot is pretty much a circle or a 2-sphere, so is a closed string, maybe a bit more irregular but approximatly the same. Of course more is needed to identify the closed string as an unknot than the shape. I assume that it is not so, yet I have no reason to deny it. I hope you may give me a...
  17. Stephanus

    Closing Threads on Physics Forums - Steven's Inquiry

    Dear staff, I just read an interesting thread: https://www.physicsforums.com/threads/can-you-check-my-equation.827896/ The thread was created yesterday 16 August 2015. But now, 17 August 2015 is already closed. I see no offending content, no protest of the mentors, but it's closed anyway. Can...
  18. S

    Statics: tension in cable holding gate closed

    1. Homework Statement The tension in the cable is 800LBs. Find the depth of water that produces this tension. The gate is hinged at B; the cable is attached at A. (Figure 1)Homework EquationsThe Attempt at a Solution OK, so this is just 2 opposing lever arms: the tension in the cable is...
  19. Neptune2235

    Closed Universe: Can Universe Be Considered a System?

    This is probably a silly question, but it's summertime and I can't ask my professor. If the universe turned out to be closed (even in light of WMAP's findings), would it be possible to consider the entire universe a closed system?
  20. G

    Closed loop problem for lighting in thunderstorm?

    Hello. As far as I know, every circuit capable to flow current must be closed. In other word, open circuit can not flow the current, obviously. Right now, I would like to know this is also true for lighting in bad weather. When bottom of the dark and heavy cloud get more and more electron by...
  21. Rasalhague

    Proving that Every Closed Set in Separable Metric Space is Union of Perfect and Countable Set

    Homework Statement Prove that every closed set in a separable metric space is the union of a (possibly empty) perfect set and a set which is at most countable. (Rudin: Principles of Mathematical Analysis, 2nd ed.) Homework Equations Every separable metric space has a countable base. The...
  22. P

    Mean value theorem, closed intervals

    Mean Value Theorem Suppose that ##f## is a function that is continuous on ##[a,b]## and differentiable on ##(a,b)##. Then there is at least one ##c## in ##(a,b)## such that: $$f'(c) = \frac{f(b) - f(a)}{b - a}$$ My question is: wouldn't it be better to state that ##c## is in ##[a,b]## rather...
  23. C

    Can closed wing aircraft take off as hydrofoil

    Mildly futuristic setting concerning technology, sparsely populated exoplanet with 3 atm. I'm looking for a cool, but very practical plane design. A photo of design that I thought about (from wikipedia) : (except that I think about a bit smaller ones) It looks as if such design had two...
  24. halfgt2

    Pump Head & Suction (leaky closed system) PF Newbie

    Hi physicists! I am scratching my head to remember the most basic laws of fluid flow while I try to irrigate things from a barrel. Not exactly rocket science, I know ;-) But very exciting for me ... The situation is simply a pump (cheap submersible one) put into a barrel (sitting on the...
  25. A

    Formula for relating time and heat gained for closed system

    This is for work. I need to make a table for a client. What we did: had two different closed systems, only difference is material. We had frozen goods in both containers, the containers were both removed from the cooled surroundings they were in and placed outside. The temperatures were...
  26. L

    RF radiation out of closed steel container

    Suppose you have an RF generator feeding a vacuum system with argon ionized by that RF. With the tuner you see the VSWR is very good. That is version A, no ground or poor ground. Version B is the same thing, the container is stainless steel half inch thick to hold the vacuum. But in this case...
  27. SrVishi

    Proving Dedekind cut Multiplication is closed

    Homework Statement I am reading Rudin's Principles of Mathematical Analysis (3rd edition) and am working through the construction of ##\mathbb{R}##. In step 6 of his construction, we must first verify that the field properties of multiplication hold for how he defines multiplication for the...
  28. X

    Current requires a closed loop to flow in DC, not AC?

    It is my general understanding that according to KCL, current requires a closed loop to flow in DC. However, this is apparently not true in AC; current doesn't needa closed loop to flow. I have drawn a circuit below which causes confusion: C1 is a charge capacitor, R1 is a resistor, I1 an...
  29. S

    Double Orthogonal Closed Subspace Inner Product => Hilbert

    Let X be an Inner Product Space. If for every closed subspace M, M^{\perp \perp} = M, then X is a Hilbert Space (It's complete). Hint: Use the following map: T : X \longrightarrow \overset{\sim}{X}: T(y)=(x,y)=f(x) where (x,y) is the inner product of X. Relevant equations: S^{\perp} is always...
  30. TrickyDicky

    Descriptions of time evolution: closed vs open systems

    The equivalence between descriptions of time evolution in QM are rigorously defined and proved for conservative systems as explained for instance among many other sources in Jauch's "Foundations of quantum mechanics" in the chapter 10. However, and an exception is the cited reference, it is not...
  31. J

    Noise Issues with closed loop accelerometers

    Hi, Can anybody explain to me what the major noise issues are with mems closed loop accelerometers
  32. Shreyansh

    Electric field inside a closed conductor.

    I recently studied Gauss' theorum according to which there is no electric field inside a closed conductor. But an isolated chage emits field lines in all possible directions. So why is it that there are no electric lines from the surface of the closed conductor inside it?
  33. A

    Standing waves in tube closed tube

    Homework Statement A tone with frequency 2,00 * 10^3 Hz is held above a tube filled with water. The water level is increased and decreased. When the water level is 5.7cm below the opening of the tube, the first sound maxima is heard. When the water level is 39.3cm below the opening of the...
  34. T

    Friction loss to vertical pipes in a closed system?

    So in designing closed systems, mostly heating systems, I realized today that I've probably been doing one thing wrong all these years. In such a system one doesn't take elevation loss due to gravity into account since you "get it back" on the way down. This I've always been aware of, but what...
  35. E

    Conservation of heat on a closed system

    Homework Statement Hey folks, anyone who can help me with this one get a massive shoutout. Here goes: 75 kg of water at 45 degrees celsius is "mixed" with 70 kg of Aluminum at 2600 Degrees Celsius. What is the final state of both system and how much, If any, of liquid water will be left Assume...
  36. J

    Electromagnetic induction of a closed circular wire

    Homework Statement (See image) a closed circular wire A lies in the plane of the wire B in the circuit. Deduce the direction. Of the induced current in A when (A) the switch is closed (B) the switch is opened (C) the wire A is raised out of the plane of the paper. Homework EquationsThe...
  37. M

    Are there closed curve solutions for these ODE constraints?

    Are there closed curve solutions for ##\mathbf{v}(t) \in \mathbb{R}^3## satisfying this constraint? $$\mathbf{v}(t) \cdot \frac{d^2}{dt^2}\mathbf{v} = 0 $$
  38. Shackleford

    Calculate closed curve integral

    Homework Statement Calculate ∫C \frac{dz}{z(z+a)} where C is the unit disk Δ(1) with counterclockwise orientation where a is a complex number with |a| < 1. Homework Equations ∫L \frac{dz}{(z-p)}= 2πiν(L,p) The Attempt at a Solution Using partial fraction decomposition, ∫C...
  39. P

    Closed Discussion: Why Seal Material?

    Why should I closed the discussion "material for sealing"??
  40. anemone

    MHB Find closed form expression for a given sum

    Find a closed form expression for \sum_{k=1}^{n^2}\dfrac{n-\lfloor\sqrt{k-1}\rfloor}{\sqrt{k}+\sqrt{k+1}}.
  41. P

    Viability of closed loop deep geothermal plants?

    Hello everyone, Just posting this because I was wondering if it's possible to build 5-10km deep closed loop geothermal power plants from microgrid sizes of 1-5MWe to commercial power plant sizes of 0.5-1GWe that can have construction costs in the $3,000,000 per MWe range (similar to solar and...
  42. Hang11

    Modeling boiling in a closed container with a small hole

    I'm trying to build a mathematical model of something like Heron's Aeolipile: http://en.wikipedia.org/wiki/Aeolipile I'd like to know, based on a known heat flux, the pressure and temperature attained in the container. I assume as water boils, the control volume loses mass and energy, the...
  43. C

    Definition of a closed thermodynamical system.

    Wikipedia states the following definition of a closed, thermodynamical system: "In a closed system, no mass may be transferred in or out of the system boundaries. The system always contains the same amount of matter, but heat and work can be exchanged across the boundary of the system."...
  44. G

    Closed Timelike Curves: Exploring the Boundaries

    [Mentor's note: split from https://www.physicsforums.com/threads/gravity-instantaneous.801033/ ] If masses can not just appear and disappear, how do solutions with closed timelike curves work? If you have some mass happily looping around such curve, from some other point of view you have some...
  45. Mingsliced

    Thermodynamics - Work Done in a Closed System (Polytropic?)

    Just want to check that I've used the correct method for this thermodynamics question I've been set. Any clarification would be greatly appreciated. So I have a closed system in which a gas is compressed from a pressure of 3 bar absolute to 5 bar absolute. The volume changes from 0.9m^3 to...
  46. U

    Closed Universe - FRW Equation

    Homework Statement (a) Show that the equations satisfy FRW equations. (b) Show the metric when ##\eta## is taken as time Homework EquationsThe Attempt at a Solution [/B] The FRW equation is: 3 \left( \frac{\dot a}{a} \right)^2 = 8\pi G \rho Using ##\frac{da}{dt} = \frac{da}{d\eta}...
  47. EddieP

    Calculating the magnetic field of a closed magnetic circuit

    I am interested in calculating the magnetic field strength produced by an electromagnet with a core shaped like an O that forms a closed magnetic circuit, shown in the attached image that can also be seen here -...
  48. 1

    (Answered) Finding new potential difference after switch is closed?

    Homework Statement The problem is: A 10.0-μF capacitor is charged to 15.0 V. It is next connected in series with an uncharged 5.00-μF capacitor. The series combination is finally connected across a 50.0-V battery as diagrammed in Figure P26.63. Find the new potential difference across the...
  49. K

    Prove Set of all onto mappings from A->A is closed

    Homework Statement Prove that set of all onto mappings of A->A is closed under composition of mappings: Homework Equations Definition of onto and closure on sets. The Attempt at a Solution Say, ##f## and ##g## are onto mappings from A to A. Now, say I have a set S(A) = {all onto mappings of A...
  50. Amy Marie

    Green's Theorem and simple closed curve

    Homework Statement Use, using the result that for a simple closed curve C in the plane the area enclosed is: A = (1/2)∫(x dy - y dx) to find the area inside the curve x^(2/3) + y^(2/3) = 4 Homework Equations Green's Theorem: ∫P dx + Q dy = ∫∫ dQ/dx - dP/dy The Attempt at a Solution I...
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