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. F

    Calculate resistance if the switch is closed 2 battery with different voltage

    Homework Statement before that, can you tell me about "current flow in this circuit" if : A. the switch is open B. the switch is closed the Question is No. 1 Calculate the resistance of R if the value of the current I in the figure is 0.50 A. ( i think it is related to no 2) no 2. Calculate...
  2. F

    I Closed surfaces and closed curves

    How to know if a surface is closed ? Surfaces such as x^(2/3) + y^(2/3) + z^2 = 1 or x^6 + y^6 + z^6 = 1. Is there a way to know if these surfaces are closed ( without the help of a computer program) ? Is there a general way to know if a surface is closed ? What about curves ? How to know if a...
  3. M

    Computation of maximum pressure in heated closed vessel

    I have a relatively simple design problem but my memories of thermodynamics are very rusty and I can't figure it out on my own. To make it short, I want to put a mix of solid, water and air in a 500mL pressure vessel and heat it all up to 250'C for several weeks. T and P are at room conditions...
  4. M

    Based Sketches, Closed Profiles and Self-Intersection

    Would you please explain what "closed profiles" mean and what self-intersection is? "Both single and multiple sketches may be used as the base objects for this feature.Base sketches must include closed profiles and may not be self-intersecting." Would you explain what "base sketches", "base...
  5. Pushoam

    B Closed surface bounding a volume V

    Is a surface bounding a volume always a closed surface?
  6. Muaadh

    I Application of resonance in one end closed pipe in real life

    Hello, My name is muaadh. I had an experiment in Physic about resonance in one end closed pipe. Our homework is to find applications in real life about this experiment. This photo of our experiment.
  7. M

    Conservation of mass relation for a closed system

    Source: Çengel/Cimbala. Above part is confusing for me from some points. First of it what can a closed system refer to? I just understand a piston/cylinder arrangement with an ideal gas in it. But this concept must be more comprehensive than I have it in my mind. Second, does "closed system...
  8. Mr Davis 97

    If F is algebraically closed, show Alg ext is closed too

    Homework Statement Let E be an algebraic extension of F in which every polynomial in F[x] can be factored into linear polynomials. Then E is algebraically closed. Homework EquationsThe Attempt at a Solution This seems like a very easy problem, but I'm not sure how to write things down formally.
  9. A

    Why does this bulb get brighter after the switch is closed

    Homework Statement Homework Equations None The Attempt at a Solution The answer is B, bulb B will be brighter than before. My thought was that initially, the current gets split so that 2/3 I0 goes to the branch with 2 bulbs, since it has twice the resistance of the first branch, and that...
  10. whatphysics

    Finding closed loop gain and Ip and In current in op amp

    Homework Statement Finding closed loop gain and Ip and In current in op amp Homework Equations - The Attempt at a Solution I started by trying getting voltage divider for points between R1 and R2 as (R2/(R2+R1))Vs and between R4 and R5 similarly. And I'm not sure how to continue on. Any help...
  11. gelfand

    Why Does a Car Accelerate When Rolling Down a Hill?

    [Mod note: Thread moved from General Discussion forum, so no homework template is shown] So - I've no idea where to write this but... I was looking at this post : https://www.physicsforums.com/threads/car-rolling-down-a-hill.302812/ And started to answer it as it was similar to some stuff...
  12. T

    Resonance at low and high frequencies of 2 closed end tubes

    Homework Statement The figure (attached) shows two tubes that are identical except for their slightly different lengths. Both tubes have one open end and one closed end. A speaker connected to a variable frequency generator is placed in front of the tubes, as shown. Te speaker is set to produce...
  13. V

    Closed form solution for second order beam deflection?

    Homework Statement A beam of length L is fixed on one end and roller supported on the other end. An axial force P is applied on the ends of the beam. The beam is loaded with a uniform distributed load (q) along its entire length. The beam has constant EI. Find an expression for the maximum...
  14. J

    ControlSystems - Easy way to simplify Closed Loop Equation?

    Homework Statement ##G_{OL} = \frac{5}{s}## ##G_{CL} = \frac{KG_{OL}}{1+KG_{OL}}## Homework EquationsThe Attempt at a Solution It's pretty easy when the equation is so simple ##G_{CL} = \frac{K\frac{5}{s}}{1+K\frac{5}{s}}## ##G_{CL} = \frac{5K}{s+5K}## If the open loop equation is really...
  15. I

    I Need closed form for a Binomial series

    Hello I was solving a problem in probability. Here is the statement. Seven terminals in an on-line system are attached to a communications line to the central computer. Exactly four of these terminals are ready to transmit a message. Assume that each terminal is equally likely to be in the ready...
  16. HethensEnd25

    An ideal gas closed system reversible process

    Homework Statement an Ideal gas at T = 70 C and 1 bar undergoes following reversible processes: a: Adiabatically compressed to 150 C b: then, cooled from 150 to 70 C at constant pressure c: finally, expanded isothermally to the original state (T=70 C and P = 1 bar) Homework Equations...
  17. J

    Calculating Capacitance in Closed Loop Circuits

    Homework Statement Homework Equations C=Δq/VThe Attempt at a Solution So part a: The capacitance of 3 should be the difference in charge of b and a divided by the voltage of the circuit? C3=(14μC-6μC)/12V =6.67*10-7 F This was wrong...
  18. Dorian Black

    Magnetic forces within a closed ferrous core

    If a toroidal ferrous core has a number of windings round it and a DC current going through them, would this magnetic core be subjected to a 'shrinking force'? To phrase it more clearly, if the toroidal core was compressible, would it actually get compressed? On the one hand, since the...
  19. Mr Davis 97

    I For groups, showing that a subset is closed under operation

    To show that a subset of a group is a subgroup, we show that there is the identity element, that the subset is closed under the induced binary operation, and that each element of the subset has an inverse in the subset. My question is regarding showing closure. To show that the subset is closed...
  20. Mr Davis 97

    Showing that a subset is closed under a binary operation

    Homework Statement Suppose that * is an associative binary operation on a set S. Let ##H=\{a \in S ~| ~a*x=x*a, ~ \forall x \in S\}##. Show that * is closed under H. Homework EquationsThe Attempt at a Solution Let b and c be two different elements in H. We need to show that b*c is also in H...
  21. S

    A Feynman rule for closed fermion loop in QED

    One of the Feynman rules of QED is the following: For a closed fermionic loop, the Feynman rule is to start at an arbitrary vertex or propagator, follow the line until we get back to the starting point, multiply all the vertices and the propagators in the order of the line, then take the trace...
  22. sa1988

    "Show B is closed if and only if...." (More Topology....)

    Homework Statement Let ##A## be a subspace of a topological space ##X##, and let ##B\subset A##. Show that ##B## is closed if and only if there exists a closed subset ##C \subset X## such that ##B = C \cap A## Homework EquationsThe Attempt at a Solution So I've started by just drawing the...
  23. whatphysics

    Finding closed loop gain in ideal op amp

    Hello there, this isn't necessarily a homework question. I came across this qn during revision and didn't know how to solve it. Any help would be greatyly appreciated. The answer is 0.97 1. Homework Statement For the ideal OP-Amp in negative feedback configuration shown in Figure Q30...
  24. P

    A Closed form for series over Exponential Integral

    Is there a closed form for the constant given by: $$\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(2))}{n}$$ (Where Ei is the exponential integral)? Could we generalize it for: $$I(k)=\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(k))}{n}$$ ? My try: As it is given that k will be a positive integer, I have...
  25. P

    I Winding number for a point that lies over a closed curve

    The definitions of the winding number, that I have found, do not consider the case in which the point lies over the curve. Is there the winding number undefined ? I'm interested in this issue because I'm writing an algorihm for polygon offsetting that as first step creates a row offset polygon (...
  26. Oedipus

    I Closed form solution for this integral

    After series of algebraic simplifications, I ended up with the following integral: ##\int_0^\infty \exp(-Kx) \arctan(x) dx ## As far as I searched, there is no closed form solution for the integral. But, K is my design variable that I need to optimize later. To do this, I need to take K out of...
  27. Andrew Pierce

    Thermodynamics piston-cylinder closed system

    Homework Statement An insulated piston-cylinder device contains 5 L of saturated liquid water at a constant pressure of 175 kPa. Water is stirred by a paddle wheel while a current of 8 A flows for 45 min through a resistor placed in the water, If one-half of the liquid is evaporated during this...
  28. O

    A Understanding Exact vs. Closed Forms for Mechanical Engineers

    (I am a mechanical engineer, trying to make up for a poor math education)' I understand that: A CLOSED form is a differential form whose exterior derivative is 0.0. An EXACT form is the exterior derivative of another form. And it stops right there. I am teaching myself differential forms...
  29. Marcus95

    Number of Different resonances in a closed Box

    Homework Statement Show that the possible resonance frequencies in a 3D box with side a are constant multiples of ##(l^2+m^2+n^2)^{1/2}##, where l, m and n are integers. Assume that the box with sides a is filled with a gas in which the speed of sound is constant. Hence show that the number of...
  30. G

    I Open or closed Casimir system?

    If you had the Casimir effect pushing two plates together, would that be an open or closed system? And why? I haven't been able to find a satisfying answer/explanation to that.
  31. kostoglotov

    Finding the closed form of a recursive LTI system

    Homework Statement Find the closed form of the impulse response of the system y[n] = 7y[n-1]-12y[n-2]+x[n] using the peel away and guess method. Ie, by using Python code to find the geometric ratios and amplitudes of the outputs as n grows large, then calculate residuals, and find the...
  32. B

    Proving a Certain Set is Closed in the Uniform Topology

    Homework Statement Let ##Q = \{(x_1,x_2,...,) \in \mathbb{R}^\omega ~|~ \lim x_n = 0 \}##. I would like to show this set is closed in the uniform topology, which is generated by the metric ##\rho(x,y) = \sup d(x_i,y_i)##, where ##d## is the standard bounded metric on ##\mathbb{R}##. Homework...
  33. J

    Closed trajectories for Kepler with spin-orbit corrections?

    Kepler problem explains closed elliptic trajectories for planetary systems or in Bohr's classical atomic model - let say two approximately point objects, the central one has practically fixed position, they attract through 1/r^2 Newton's or Coulomb force. Kind of the best motivated expansion we...
  34. M

    MHB How could we show that D is bounded and closed?

    Hey! :o Let $D\subseteq \mathbb{R}$ be a non-empty set. I want to show that $D$ ist compact if and only if each continuous function is bounded on $D$. I have done the following: We suppose that $D$ is compact. Since $f$ is continuous, we have that $f(D)$ is also compact, right? (Wondering)...
  35. F

    Angle of twist / stress of thin wall having closed section

    Homework Statement why the mean area enclosed within the boundary of the centerline of tube thickness is (0.035)(0.057) ? Is it wrong ? Second question , why for the ds it's 2(57) and 2(35) respctively ? what is ds actually ? Homework EquationsThe Attempt at a Solution for the first...
  36. A

    Compressibility/Expansion in a closed system

    Howdy. Long time reader first time posting. Usually try to solve these problems on my own but this one has caused a few sleepness nights already so looking for some insight. The attached shows a simplified schematic of what I am dealing with. It is basically a hydraulic cylinder with the...
  37. G Cooke

    I Can Temperature Changes Alter Humidity in a Completely Filled Closed System?

    We know that for a closed system, isobaric heating decreases the humidity and isothermal compression increases the humidity. But assuming that we start with the volume completely filled with humid air, is it not true that any increase in temperature must also increase the pressure? If so...
  38. T

    Find magnetic flux density B circulation in closed contour

    Homework Statement Find magnetic flux density B circulation in closed contour. The countour consists of square with a perimeter of 4b. It includes a square conductor with a perimeter of 4a. A homogenic current flows through a conductor with a current density of j. Homework Equations...
  39. Z

    I Proof check: S in C Compact implies S is closed and bounded

    I am using Lang's book on complex analysis, i am trying to reprove theorem 4.1 which is a simple theorem: Let Compact(S \in \mathbb{C}) \iff Closed(S) \land Bounded(S) I will show my attempt on one direction of the proof only, before even trying the other direction. Assume S is compact Idea...
  40. I

    Proving that three closed orbits must contain a fixed point

    A smooth vector field on the phase plane is known to have exactly three closed orbit. Two of the cycles, C1 and C2 lie inside the third cycle C3. However C1 does not lie inside C2, nor vice-versa. What is the configuration of the orbits? Show that there must be at least one fixed point bounded...
  41. A

    Pressure at the closed end of a pipe with a leak?

    Suppose I have an air pipe that is used for "grasping" other objects using negative pressure. When an object is grasped, assume it is a perfect seal and that end of the pipe is closed. On the other end of the pipe is the pressure source creating the vacuum. Somewhere in the middle is a short...
  42. Grinkle

    B Does QM allow for entropy decrease of a closed system?

    I recently posted a statement that according to the 2nd law of thermodynamics, entropy always increases in a closed system, no matter how small the time interval is that one looks at. I think that is true for classical thermodynamic models, please correct me if I am wrong. Does quantum...
  43. moenste

    Reading of the voltmeter with closed switch

    Homework Statement (a) In the circuit shown below E is a cell of source (internal) resistance r and the resistance of R is 4.0 Ω. With the switch S open, the high resistance voltmeter reads 10.0 V and with S closed the voltmeter reads 8.0 V. Show that r = 1.0 Ω. (b) If R were replaced by a...
  44. Phylosopher

    I Why is Stoke's theorem of a closed path equal to zero?

    Hello,I had a discussion with my professor. He tried to convince me but I couldn't understand the idea. The Stokes Theorem (Curl Theorem) is the following: My professor says that the value of the equation should be zero whenever the area of integration is closed! (which will make a volume in...
  45. K

    MHB Extreme points of L^p[0,1] on unit closed ball

    I would like to prove that if $\|f\|_p = 1$ then $f$ is extreme point of unit closed ball in $L^p[0,1]$. [here $1<p<\infty$] I suppose we should try to prove it by contradiction. That is, if $f \in L^p$, with $\|f\|_p=1$, is not extreme, then exists $g,h \in L^p$ with $\|g\|_p,\|h\|_p \leq 1$...
  46. arupel

    I Intersection & union of closed and open sets?

    I am a little confused here: a) The number 2 which is at the beginng of one set is closed. The number 2 is open at the beginning of the other set. b) The number 2 is closed of the beginning of a set which goes to infinity. The other set begins at 0 and goes to infinity (2 is an...
  47. T

    Does a Magnetic Moment μ exist for any closed current loop?

    I'm asking the above question as I imagined a current loop made out of a curving wire that cannot fit into a flat plane. Where does the direction of μ point then? Also, is there only one μ value for any current loop, independent of the chosen axis of tilting? Or can a current loop have...
  48. A

    Vapor Pressure In Closed Cylinder

    Hi There, I am trying to understand if I have a vacuum in the below scenario or simply just really low pressure. A pump supplies a pipe with a constant supply of water at one end (Point A) the water discharges several kilometers away at some lower elevation (Point B). At "Point A" a valve...
  49. T

    Linear Algebra, subset of R2 not closed under scalar multipl

    Homework Statement Construct a subset of the x-y plane R2 that is (a) closed under vector addition and subtraction, but not scalar multiplication. Hint: Starting with u and v, add and subtract for (a). Try cu and cv Homework Equations vector addition, subtraction and multiplication The...
  50. JulienB

    Difference between closed set and open set is a closed set

    Homework Statement Hi everybody! I'd like to check with you guys if I tackled that problem correctly. I might have a few theoretical questions along the way :) Prove that the difference ##A \setminus B## of a closed set ##A \subset \mathbb{R}^2## and an open set ##B \subset \mathbb{R}^2## is...
Back
Top