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. bob012345

    Why are So Many 'Hot Threads' Closed?

    A lot of 'hot threads' come up yet when I go there the discussion is already closed. Very frustrating. If you pour cold water on the discussion it's no longer a hot thread.
  2. paulb203

    B When is a polygon not a polygon?

    For a shape to qualify as a polygon does it have to be closed. I was just introduced to frequency polygons and was surprised to see each one was a shape that wasn't closed. The definitions of polygon that I've come across go something like, a closed shape consisting of three or more lines.
  3. C

    Closed path term in Thermodynamics

    For part(a) of this problem, The solution is, a. 160 J In part (a), are they referring to the simi-circular path from R to S instead of the path from R back to R? I though the closed path would be the path from R to R, or the path from S to S, where both give W = 0 since ##W = P(V_f - V_i) =...
  4. Thomas_Kellner

    Change in temperature of air in a closed system

    Looking at the given values, I thought the specific heat formula could be used to calculate the final temperature of the air: c = Q/mΔT. Since the final temperature is the sum of the initial temperature and the change in temperature, the formula can be rearranged to ΔT = Q/m*c. Q = 30 W * 10 s...
  5. Steven Bolgiano

    I Pressure Required to Circulate Liquid in a Closed System?

    Example: 3/4 pvc in closed circuit with pump. Linear distance of pipe=30ft / head 8ft .... so not counting friction, what general description of force can describe what's required to make the liquid circulate?
  6. mastermechanic

    Electronics How to control a stepper motor in closed loop (PID) in arduino?

    Hello, What I have I have a NEMA17 stepper motor driven by a DRV8825 driver module, an arduino uno, a multiturn potentiometer. What I want to do I want to control the stepper motors in a PID closed loop. The motor shaft will be connected to the potentiometer and I will be sure that the motor...
  7. P

    A Why electromagnetic tensor (Faraday 2-form) is exact? (and not closed)

    Following from Wikipedia, the covariant formulation of electromagnetic field involves postulating an electromagnetic field tensor(Faraday 2-form) F such that F=dA where A is a 1-form, which makes F an exact differential form. However, is there any specific reason for expecting F to be exact...
  8. C

    I In a closed loop system with a pump, how can we control the pressure?

    How can we control the pressure of the water inside a closed loop system (chiller system for example)? Let´s say, we have a pump curve and an system resistance curve that can be modified (through opening or closing some valves) In everywhere, what I see is that the intersection of the system...
  9. I

    Physics of Water in the Closed System of the Great Pyramid

    Hello, I am working on a theory for a Great Pyramid power plant and I need some help understanding if my current hypothesis is even possible and how to calculate how much water will fill the upper structure. I believe the water system to work as follows: An aqueduct delivers a steady flow of...
  10. A

    I Fluid flow through a pin-hole of x diameter in a closed container

    Greetings, I've come across lots of exercises regarding Bernoulli's equation. However, never seen one where the top of the vessel is closed, and fluid flow exists via gas (air) going in. Has this problem been studied in the past? Assume a cylindrical vessel filled to the maximum with a D-sized...
  11. Arne

    I Assumptions about the convex hull of a closed path in a 4D space

    Hello everyone, I am struggling to get insight into a certain set in 4D space. Given is a closed path in 4D-space with constant Euclidean norm $$\vec{\gamma} (\theta):[0,2\pi]\to\mathbb{R}^4, \ \ \vec{\gamma}(0)=\vec{\gamma}(2\pi), \ \ ||\vec{\gamma}(\theta)||_2 = \mathrm{const.}$$ I am looking...
  12. T

    I Closed Form for Complex Gamma Function

    Hey all, I was wondering if there was an equivalent closed form expression for ##\Gamma(\frac{1}{2}+ib)## where ##b## is a real number. I came across the following answer...
  13. P

    How to model the behavior of a closed loop position system?

    Hello everyone, I would need help to model a motorized system controlled in a closed loop. It is a personal project. At first, I am looking to obtain the transfer function and simulate the system on computer. In a second step (not the aim of this thread), I would like to use this simulation to...
  14. T

    Stewart platform and closed loops

    Hello! (I am not asking for someone to do this for me. I am only asking a qualitative question.) Suppose one knows the lengths of all six links that are involved in the Stewart platform. Is that enough to define the position and orientation of the top (assuming the base is fixed) I would...
  15. M

    I Water bath and water vapor + air mixture in a closed system

    Hello, At my work I came up with the following question: Say we have a vacuum chamber. Inside the vacuum chamber we have at the bottom a water bath. The rest of the chamber is filled with a air and water vapor mixture. The whole system is placed in a room, is at room temperature and is in...
  16. hxtasy

    Gerotor pump, will it work in a closed system without air?

    just hypothetical question, First off I am not very knowledgeable in pumps. Let's say you have a pump to pump fluid, i don't think the type matters, self priming as I understand it creates a vacuum with the air in the system to pull the fluid towards the gear pumps. I'm wondering what happens...
  17. Purplepixie

    MHB Closed form solution to sum of sine positive zero-crossings

    Hello, I would like to know, if there's a closed form solution to the following problem: Given a sum of say, 3 sines, with the form y = sin(a.2.PI.t) + sin(b.2.PI.t) + sin(c.2.PI.t) where a,b,c are constants and PI = 3.141592654 and the periods in the expression are multiplication signs, what...
  18. junyoung

    I Open interval or Closed interval in defining convex function

    The Korean textbook standard defines the convexity of the function as an open section. Many textbooks and university calculus textbooks define the convexity of the curve as an open section. However, some textbooks define convexity as closed sections. Do you think it is right to define the...
  19. WMDhamnekar

    MHB Proving $\displaystyle\int_C \vec{F}\cdot d\vec{r} = 0$ with Closed Curve

    If C is the simple closed curve in the xy plane not enclosing the origin, how to prove that $\displaystyle\int_C \vec{F}\cdot d\vec{r} =0 $ where $$ F= \frac{yi +xj}{x^2+y^2}$$ How to answer this question? Any math help will be accepted. I am working on this question. If any member of Math...
  20. tworitdash

    MATLAB Closed form not the same as the discrete form

    clear; lambda = 3e-2; x = 4 * pi/lambda * linspace(eps, 15, 100000); T = 5e-3; t = [0:0.001e-3:T] ; % 0.1:1e-3:0.1+T]; u = 3; a = 4*pi/lambda * u; for i = 1:length(x) Z(i) = sum(-((cos(a.*t) - cos(x(i).*t)).^2 + (sin(a.*t) - sin(x(i).*t)).^2)); end % Z1 = csc((a+x)/2) .*...
  21. Question69

    I Alexander Vilenkin and energy of a closed universe

    For reference:
  22. J

    B How is efficiency defined in rocket propulsion?

    Whicle has 4 wheels, inside is oval closed room with fan that blow inside air to the wing. Wing produce difference in static pressure in direction of travel. Will vehicle move forward or not? If I look just at pressure difference at wing, vehicle will move forward but I know from Newton 3 law...
  23. C

    I In Euclidian space, closed ball is equal to closure of open ball

    Problem: Let ## (X,d) ## be a metric space, denote as ## B(c,r) = \{ x \in X : d(c,x) < r \} ## the open ball at radius ## r>0 ## around ## c \in X ##, denote as ## \bar{B}(c, r) = \{ x \in X : d(c,x) \leq r \} ## the closed ball and for all ## A \subset X ## we'll denote as ## cl(A) ## the...
  24. A

    Difference between a closed solid and a Cartesian surface

    Greetings All! I have hard time to make the difference between the equation of a closed solid and a cartesian surface. For example in the exercice n of the exam I thought that the equation was describing a closed solid " a paraboloid locked by an inclined plane (so I thought I could use...
  25. physicslover2012

    Standing Waves in a tube closed at both ends

    During our classes, we haven't discussed the situation of a tube closed at both ends. But, assuming the position of the nodes and antinodes, I think it's a case similar to the one where the tube is open at both ends, so I think that f = v/λ = nv/(2L). Using the numeric data, my frequency would...
  26. ergospherical

    Justifying the peak closed loop gain of an op-amp circuit

    I'm just looking at a Bode plot of log(gain) vs log(frequency) for a an amplifier circuit. I'm trying to figure out whether I'm expecting to see a resonance in the gain at the frequency where I measured one. How could I, in principle, work out theoretically where the peak gain should occur - is...
  27. B

    B Conservation of momentum in a closed system

    In a closed system consisting of a set of particles not at rest relative to each other and acting on each other only by classical mechanical collision (i.e. billiard balls model, not including gravity or other long-range interactions), does conservation of momentum imply that the system will...
  28. brotherbobby

    A line integral about a closed "unit triangle" around the origin

    Problem statement : As a part of the problem, the diagram shows the contour ##C##above on the left. The contour ##C## is divided into three parts, ##C_1, C_2, C_3## which make up the sides of the right triangle. Required to prove : ##\boxed{\oint_C x^2 y \mathrm{d} s = -\frac{\sqrt{2}}{12}}##...
  29. anubhavsingh

    CMRR in open loop and closed loop configuration of opamp

    For an opamp in open look configuration, Here Ad should be equal to open loop gain of opamp and Now consider the closed loop config of opamp (negative feedback used): However, Ad is closed loop gain here (according to Sedra Smith) and In terms of open loop gain, A is open loop gain...
  30. K

    A Hooke's law, Bertrand's theorem and closed orbits

    Bertrand's Theorem says : the only forces whose bounded orbits imply closed orbits are the Hooke's law and the attractive inverse square force. I'm looking at the hookes law ##f=-k r## and try to see explicitly that the orbit is indeed closed. I use the orbit equation ##\frac{d^{2} u}{d...
  31. R

    B Free fall floating in a closed spaceship near a gravity source

    Floating inside a closed spaceship, no windows, not knowing if I'm free falling near a gravity source or far away from any gravity source, are there any experiments that can be made, to determine if there is a gravity source near and if there is such an experiment, to determine the gravity...
  32. docnet

    Prove that the intersection of subspaces is compact and closed

    Given that one of the ##S_i## (let's name it ##S_{compact}##), is compact. Assume there is an open cover ##\mathcal V## of ##S_{compact}##. By definition of a compact subspace, there is a subcover ##\mathcal U## with ##n<\infty## open sets. Notice that ##\forall x\in (\bigcap_i S_i)##, ##x\in...
  33. G

    Plug the Closed Ends of a Pipe at Depth and Bring it to the Surface

    Hi Guys - I have very simple question but I cannot get my head around. Say if we cut pipeline into one section (12m) then close each cut end with temporary plugs Water depth is 100m. Before the cut there is seawater inside the pipeline. Now I understand there is no differentiated pressure...
  34. kmot

    I Why is this closed line integral zero?

    This problem comes from fluid dynamics where Kelvin circulation theorem states, that if density "rho" is a function of only pressure "p", then closed line integral of grad(p) / rho(p) equals zero. It seems so trivial, so that no one ever gives reason for this claim. When trying to solve it...
  35. M

    I Calculating Windspeed after Brick Launch from Dumpster Lid

    Hello, We had a wind storm. We have a dumpster with a lid. On that lid we put a heavy brick to keep the lid closed during wind storms. It's worked great for years. But we had a very strong wind storm and it launched that brick quite a distance. I'm trying to figure out the wind speed that would...
  36. Demystifier

    I An open set can be a closed interval?

    I am confused with some basic definitions in general topology. Topological space is defined as a set ##X## and a collection ##T## of its subsets that satisfies some general properties (which I will not list here, but I will assume that the reader knows them). But such a very general definition...
  37. E

    I The energy of a closed universe is zero

    In a globally hyperbolic spacetime you have a global time ##t: M \longrightarrow \mathbf{R}## which foliates it into Cauchy surfaces ##\Sigma_t## and the metric can be written ##\mathrm{d}s^2 = -N^2 \mathrm{d}t^2 + h_{ij}(\mathrm{d}x^i + N^i \mathrm{d}t)(\mathrm{d}x^j + N^j \mathrm{d}t)##. By...
  38. barryj

    Chemistry Pressure of gasoline in a closed container

    If I knew how much of the gasoline evaporated, then I could use p = nRT/V to fine the partial pressure of the gasoline and add it to the pressure of the atmosphere. So my question is, How do I find how much of the gasoline will evaporate. I would think that the gasoline would evaporate until it...
  39. C

    Why a 20 Ohm lightbulb won't light up in a closed circuit?

    When using the voltmeter and ammeter to investigate the circuit, it was found that the batter had a current of 0.67 A, the two 30 Ω bulbs had a current of 0.17 A, and the two 10 Ω bulbs had a current of 0.50 A. In terms of voltage, each bulb had a voltage of 5 V. When the switch was closed, the...
  40. Cerenkov

    B How can the Observable Universe be a closed system?

    https://www.physicsforums.com/threads/is-the-universe-a-closed-system.620503/ Hello. I was looking back at this thread from 2012 and, to be honest, I'm a bit confused. Quoting Drakkith... To our knowledge it is. At minimum you could count the observable universe as a closed system because...
  41. W

    A Is there a closed form solution to Kepler's problem?

    Kepler's equation is M = E - e*sinE According to wiki - Kepler's equation - "Kepler's equation is a transcendental equation because sine is a transcendental function, meaning it cannot be solved for E algebraically. Numerical analysis and series expansions are generally required to evaluate...
  42. L

    MHB Is an increasing monotonic function in a closed interval also continuous?

    Hello all, Is this statement true ? Is every increasing monotonic function in a closed interval also continuous ? How do you prove such a thing ? Thank you !
  43. E

    I Stratification of air in a closed system vs the stack effect

    In thinking about temperature stratification of air: I assume that in a truly closed system with no heat inputs, air would NOT stratify by temperature. On the other hand, a heat source introduced in a closed container would generate stratification while it was generating heat (and following for...
  44. M

    MHB Set is closed as for multiplication of matrices

    Hey! 😊 We have the matrices \begin{equation*}s:=\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}, \ d:=\frac{1}{2}\begin{pmatrix}-1 & -\sqrt{3} \\ \sqrt{3} & -1\end{pmatrix}\end{equation*} and the points \begin{equation*}p:=\begin{pmatrix}2 \\ 0 \end{pmatrix}, \ q:=\begin{pmatrix}-1 \\ \sqrt{3}...
  45. L

    Magnetic Flux through a Closed Surface and Maxwell's laws

    Hi everyone, I have a question about Maxwell's laws. According to Maxwell the magnetic flux of a magnetic field through a close surface is 0. But his third law says the circuitation of an electric field depends from magnetic flux variation. I can't understand how this can be possible since...
  46. Jason-Li

    Why Does Increasing G in a Control Loop Cause Vo/Vi to Approach Unity?

    Hi all Physics Forum User, I am again coming to you to ask for help. For the above question I can't make sense of how a larger G will cause Vo/Vi to approach 1. For this I'll call Vo=V and Vi=I As can be seen from the control loop B = A*H and V = B*K hence V = A*H*K Also A = I - C and...
  47. kyphysics

    Closed vs. Open Crawlspace & Automatic Vents vs. Dehumidifer?

    So, my dad (non-scientist) was debating with his cousin over whether he needed to spend $$$ on a crawlspace dehumidifier and get closed vents. It was both a heated/fierce debate and interesting. Mostly, I just listened to two old dudes arguing in partial amusement, but some intrigue as well...
  48. M

    Engineering Closed Loop Stability Criterion: Find the values for closed loop stability

    Hi, I was just working through a closed loop stability problem in Control Theory and I don't really understand how the answer has arrived at the solution so quickly. Problem: We are working with the closed loop transfer function: $$ P(s) = \frac{K(s) G(s)}{1+K(s)G(s)} $$, where $$ G(s) =...
  49. S

    Centrifugal pump behavior when the outlet is closed

    What would happen if the water pump output or outlet is closed and pump continues running. Will the rotor or impeller inside just rotate and rotate slowly just raising temperature of stuck water in the impeller or would there be sudden increase in pressure immediately damaging the seal. This is...
  50. Math Amateur

    I Outer measure of a closed interval .... Axler, Result 2.14 ....

    I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help with the proof of Result 2.14 ... Result 2.14 and its proof read as follows: In the above proof by Axler we read the following: " ... ... We will now prove by...
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