Closed Definition and 1000 Threads

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. 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...
  2. Tareq Naushad

    Medical Why we think better with closed eyes? What about a blind person?

    To think something with full concentration I close my eyes. I believe many people also do it. It seemed to work and generates good thoughtful results. May be because with eyes closed brain is free to handle the billions of photons coming from eyes. In a noise-free room concentration should be...
  3. Tareq Naushad

    Medical With eyes closed or in a dream do we see video-like movements?

    We see real movements, we see videos, we see still photos. When we close our eyes and try to visualize some events like my son is running or sea wave or storm etc. do we visualize the movements or images with a very low frame per second(fps). In dream also we see so many events but are those...
  4. R

    [Linear Algebra] Closed formula for recursive sequence

    Homework Statement Homework Equations a) the one given b) det(A-λI) = 0 find λ values using A c)use λ values to find eigenvectors The Attempt at a Solution This wasn't explained well enough so I can understand it in class. So far, I made the matrix being multiplied to A have the following...
  5. E

    Cooling Water in a Closed Container

    I have a bit of confusion about a closed container scenario. First, I'll start with the open container. Say water is at some temperature, exposed to low humidity atmosphere, and begins to evaporate. The water that evaporates diffuses never to return to the container. To find the final...
  6. G

    I Why are total orbital QN l,m zero for closed subshell?

    Hello. Here, I'm asking why total orbital quantum number l and total magnetic quantum number m are zero for closed subshell in atom. Let me review the addition of angular momentum first: Each electron has its own orbital quantum number li and magnetic quantum number mi. Then for two electrons...
  7. Z

    Java NetBeans:Operation not allowed after resultset closed

    Hi, I am trying to access a database using netBeans.I am using the 'select' query. I have got only one record. I am displaying its only two fields in the jTextField. I have a button (next) component. I have written its handler which is used to traverse the resultset. In the constructor i am...
  8. H

    Why Reynolds Stress vanishes on boundary of closed volume?

    The rate of working of the Reynolds Stress can be written as: where ui is the fluctuating velocity and Ūi is the time-averaged velocity. It is stated in the textbook that, if we integrate the above equation over a closed volume V, the divergence term on the left integrates to zero since τRij...
  9. stevendaryl

    I Asymptotic Behavior of Modified Bessel Functions

    Does anyone know whether the following integral has a closed-form solution? If not, is anything known about the asymptotic behavior? f(x) = \int_{-\infty}^{+\infty} \frac{e^{iux}}{\sqrt{u^2 + 1}} du
  10. Math Amateur

    MHB How Does Algebraic Closure Extend to Multivariable Polynomials?

    Dummit and Foote in their book Abstract Algebra give the following definition of an algebraically closed field ... ...From the remarks following the definition it appears that the definition only applies to K[x] ... Does it also apply to K[x_1, x_2], K[x_1, x_2, x_3], \ ... \ ... \ , K[x_1...
  11. Math Amateur

    I Algebraically Closed Fields

    Dummit and Foote in their book Abstract Algebra give the following definition of an algebraically closed field ... ... From the remarks following the definition it appears that the definition only applies to ##K[x]## ... Does it also apply to ##K[x_1, x_2], K[x_1, x_2, x_3], \ ... \ ... \ ...
  12. Z

    A A discord in analysis of a closed vs. open system model

    Is there anywhere in physics textbooks , or anywhere else, a section on KINETICS OF ROTATING FLEXIBLE, CONSTRAINED BODY BY GRAVITY ( TURBINE ROTOR IN BEARINGS), NON-INVARIANT (Time -translation invariance by Noether’s theorem), WITH ECCENTRIC MASSES, TORQUE DRIVEN AT NON-CENTROIDAL AXIS...
  13. F

    How do I show that a subset is closed and convex?

    We have a vector p = (0, 0, 2) in R^3 and we have the subset S = {xp where x >= 0} + T, where T is the convex hull of 5 vectors: (2,2,2), (4,2,2), (2,4,2), (4,4,6) and (2,2,10). How do I show that the subset T is a closed and convex subset? I know that a subset is called convex if it contains...
  14. P

    What is Electrical Field in a Closed surface with no charge

    As per the Gauss Law , Net Flux Electric Field through a closed Surface (Gaussian Surface) is zero if no charge is enclosed. As per the definition of the Electrical Flux = Electrical Field Intensity dot product Area Vector i.e. Closed Integral of E.S If Electrical Flux is zero then as per the...
  15. P

    I Why does Gauss' law hold for any closed surface?

    Why does Gauss' law hold for any closed surface? and can you show this mathematically. Many thanks :)
  16. F

    Derivation of potential of two closed curves s and s'

    I am reading Maxwell's "a treatise on electricity and magnetism" and I came across a formula of "potential of two closed curves s and s' " ##M= \iint\dfrac{cos\varepsilon}{r} dsds'## where: ##M=## potential of two closed curves s and s' ##\varepsilon=## angle between elements ds and ds'...
  17. mr.tea

    I Divergence theorem and closed surfaces

    Hi, I have a question about identifying closed and open surfaces. Usually, when I see some exercises in the subject of the divergence theorem/flux integrals, I am not sure when the surface is open and needed to be closed or if it is already closed. I mean for example a cylinder that is...
  18. Ravi Singh choudhary

    Velocity of liquid from bottom pinhole of closed container

    What I know: Below link is about Torricelli's law. Velocity of liquid coming out of bottom of the tank i.e comes after using Bernoulli's equation square root of (2*g*h*) where "h" is height of fluid in the container and "g" is acceleration due to gravity...
  19. J

    Does AC form a closed loop circuit?

    Some say that AC should form a closed loop circuit for electricity utilization but is there really an loop from the Power station(hot wire) to the Ground(neutral) and then from Ground to power station so that it forms a loop?
  20. O

    A Why the terms - exterior, closed, exact?

    Hi all, (Thank you for the continuing responses to my other questions...) I am gaining more and more understanding of differential forms and differential geometry. But now I must ask... Why the words? I understand the exterior derivative, but why is it called "exterior?" Ditto for CLOSED and...
  21. M

    Parallel transportation of a vector along a closed triangle

    Hello everyone, I am trying to solve exercise 7.21 in the "Hobson, Efstathiou, Lasenby, General Relativity. An introduction for physicists." What is asked is to show that the parallel transportation of a vector, along a closed triangle on a 2-sphere, results in an vector orthogonal to the...
  22. A

    Heat transferred into a closed system

    So i am making a simple demonstration of ideal gas law using a cylinder piston system, heating the system so the piston is pushed up, i wanted to calculate the heat transferred into the system, will it be Cp(Tf-Ti) or Cp(Tf-Ti)+ work done by the system ?
  23. Q

    Function Generation, Expressing in closed forms

    Homework Statement Taking derivatives of generating functions is another useful operation. This is done termwise, that is, if F(x) = f0 + f1x + f2x2 + f3x3 + · · · , then F' (x) ::= f1 + 2f2x + 3f3x2 + · · · . For example, ##\frac{1}{(1-x)^2} = (\frac{1}{(1-x)})'= 1 + 2x + 3x^2 +· · · ##...
  24. Z

    End correction of a closed pipe

    Homework Statement Is there a scientiically approved method for end correction of a closed pipe. Homework EquationsThe Attempt at a Solution The formula used is Delta L = (3d) where d = diameter in cm.
  25. Alpharup

    B Can open sets be described in-terms of closed sets?

    Let A be an open set and A=(a,b). Can A be described, as closed set as "or every x>0, all the elements of closed set [a+x,b-x] are elements of A"?
  26. H

    Type your username in backwards with your eyes closed

    my attempt yteast
  27. J

    CO2 sublimation in a closed container

    A coworker posed a thought experiment; if you sealed a sample of frozen CO2 in an uncompressable container of identical volume and allowed it to warm to room temperature, how could it melt/evaporate, since there would be no room for the gas to expand My guess is that it would sublimate to a...
  28. fluidistic

    How can scientists trust closed source programs?

    I wonder how can scientists trust closed source programs/softwares. How can they be sure there aren't bugs that return a wrong output every now and then? Assuming they use some kind of extensive tests that figures out whether the program behaves as it should, how can they be sure that the...
  29. M

    MHB How Does E Relate to Q[x]/(x²+x+1) in Complex Algebra?

    Let, E={a+bw : a,b in ℚ) ⊆ ℂ w = -1/2 + [√(3)/2]*i ∈ C Prove: E is closed under addition, subtraction, multiplication and division (by non zero elements) Prove: E ≅ Q[x]/(x2+x+1) Is the goal to show that for any two elements in E, all 4 operations can be performed...
  30. NATURE.M

    Stuck on obtaining a closed form for parameter using MLE

    Homework Statement We have a Markov Random Field with the log likelihood as such: $$ l(\theta) = \sum\limits_{i=1}^L \log p(x^{(i)}|\theta) = \sum\limits_{i=1}^L \left( \sum\limits_{s \in V} \theta_{s} x_{s}^{(i)} - \log \sum\limits_{x} \exp \left\lbrace \sum\limits_{s \in V} \theta_{s} x_{s}...
  31. Twigg

    I Isolated/Closed Systems: Relativistic Thermodynamics Explained

    If you put everything in a rest frame, it seems as if it's impossible to tell an isolated system from a closed system (globally in SR, locally in GR). Am I off my rocker to think so? There's at least one catch I've thought of so far: light. I can't say for sure that it satisfies either...
  32. F

    Electric current passing through closed loop

    Homework Statement (sorry for possible notation errors, that might arise during the translation) Why an electric current passing through a closed loop, can be defined only in stationary conditions? Homework Equations The Attempt at a Solution I think that the reason is that, if the...
  33. R

    Applying first law of thermo to a closed spring piston

    Homework Statement A cylinder having a piston restrained by a linear spring (of spring constant 15 kN/m) contains 0.5 kg of saturated vapor water at 120ºC. Heat is transferred to the water causing piston to rise. If the piston’s cross sectional area is 0.05 m2 and the pressure varies linearly...
  34. C

    Now that all loopholes are closed

    I've read rumors that the last remaining loopholes of the Bell experiments have been closed, such as: https://uwaterloo.ca/institute-for-quantum-computing/blog/post/ask-not-which-local-hidden-variable-theory-bell-tolls-it Is this for real? And what are the surviving nonlocal realism...
  35. takgt7

    Calculating the volume in closed container?

    Hi, I have a hard time calculating volume in a closed container. Let's say, I have a flask with a volume 0.125ml, which is closed, and the pressure inside is 16.87kPa with temperature 294.7k and I did some reaction to create a gas inside the flask. The new pressure in the flask is 87.19kPa and...
  36. P

    N-spheres as closed C^inf-manifold

    Homework Statement I need to prove that the unit n-sphere is a closed C^inf-manifold, and am not sure what to do. Homework Equations The unit n-sphere is defined as: S^n = {(x_0,...,x_n) belongs to R^(n+1) | (x_0)^2+...+(x_n)^2=1} The Attempt at a Solution It's not a proof, but a simple...
  37. E

    Is there a closed form for this?

    Hi, I have this integral: \int_0^∞ \ln(1+x)\,e^{-x}\,dx Is there any closed form expression for it? Thanks
  38. H

    How Does the Wavelength Change at the Fourth Resonance in a Closed Air Column?

    Homework Statement The resonant length of a closed air column at the first resonance is 0.375m, what is the wavelength when at 4th reasonance Homework EquationsThe Attempt at a Solution 1/4λ=0.375m λ=1.5m 1.5m/7 = 0.214m
  39. David Gin

    Determing flow of a closed loop parallel pumping system

    Hi all, How would one go about determining the flow(GPM) of a closed loop parallel piping system. I believe this has to do with the pressure intake and outlet of the pump as I have a pump in the mentioned system rated at 4350GPM@50Hz but it is pumping at 4500 GPM at 37Hz, Thank you all for...
  40. nirmaljoshi

    Why flow has high velocity when partially closed?

    I want to ask why flow has high velocity when partially closed. Eg. when we partially close garden's hose pipe, the flow goes much more farther than when fully open. Supposing water is flowing through a pipe from a constant level water tank. Why flow has high velocity when partially closed...
  41. V

    Closed set with rationals question

    Homework Statement If A is a closed set that contains every rational number in the closed interval [0,1], show that [0,1] is a subset of A. Homework EquationsThe Attempt at a Solution I'm confused because for the set A = all rationals in [0,1], every point is a boundary point so the set is...
  42. N

    How I find value of U on R2 long time after switch is closed

    https://qph.is.quoracdn.net/main-qimg-c22d8aa4be4fc2ed9b2f1c7060982e04?convert_to_webp=true How to find value of U on R2 long time after switch is being closed? Capacitors are charged so there is no current going through? Or? I used kirchof rule so i get Uo+Uc1-U=0 U=Uc1+Uo...
  43. M

    Question about pressure inside closed flask

    Let's imagine that a flask is initially opened and in contact with the atmosphere. I am thinking that when the flask is closed with a lid, the air density inside will be kept the same as outside. As so, the pressure inside should remain Patm: P = (n/V).RT (n/V constant) However, shouldn't...
  44. I

    Fluid circulation around a closed curve

    I know that the circulation is defined as the counter clock wise integral around the closed curve of the flow velocity component along the curve but what is its meaning in real life? I mean what does circulation actually refer to in real life? Also could someone explain the above image? What is...
  45. F

    M,N is subset of Hilbert space, show M+N is closed

    Homework Statement [/B] Let M, N be a subset of a Hilbert space and be two closed linear subspaces. Assume that (u,v)=0, for all u in M and v in N. Prove that M+N is closed. Homework Equations I believe that (u,v)=0 is an inner product space The Attempt at a Solution This is a problem from...
  46. R

    The union of any collection of closed sets is closed?

    I don't see how this is the case. Let ao and bo be members of [A,B] with ao<bo. Let {ai} be a strictly decreasing sequence, with each ai>A and {bi} be a strictly increasing sequencing with each bi<B. Let the limits of the two sequences be A and B, respectively. Then define Ii = [ai,bi]. It seems...
  47. A

    200,000 psi closed Thread response

    Yes I fully understand that the people on this form have all of the schooling , degrees and knowledge that they have accumulated to accomplish all kinds of things. And buy my simple question, I did put on display my complete lack of knowledge in the things pertaining to my question. And you are...
  48. T

    How is a line integral over any closed surface 0?

    We just started going over line integrals in calculus, and have been told that the integral over any closed surface is 0. What I don't get is then why can we do the line integral of a circle to get 2##\pi##r? Since a circle is a closed surface, shouldn't the line integral then be 0?
  49. F

    Finding a closed form expression given decimal approximation

    Good evening. Is there a way to take a decimal approximation and see if there is a relatively simple expression? I'm guessing there might be software for this, but I'm not sure I'm even asking the appropriate question. If it matters, the number I'm after is...
  50. eryksd

    Best material for diffusing moisture into a closed vessel?

    Anyone have any suggestions on other [mold-proof] materials that might be good to diffuse moisture (distilled water) into a vessel? For a project, I am trying to create a re-humidification vessel to re-humidify certain materials that have dried out, and am trying to think of the best material...
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