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. H

    An Interval that is both open and closed.

    Homework Statement Let I C R be an interval which is open and closed at the same time. Prove that I=R or I is the empty set. Homework Equations The Attempt at a Solution I'm looking more for a outline structure for the solution. I have made assumptions that I is not equal to R...
  2. S

    [Thermodynamics I] Adding heat to a closed, rigid tank

    Homework Statement A closed, rigid tank contains 2kg of water initially at 80 degrees C and a quality of .6. Heat transfer occurs until the tank contains only saturated vapor at a higher pressure. Kinetic and potential energy effects are negligible. For the water as the system, determine...
  3. T

    What is the Closed Form of the Power Series 1+3x+6x^2+10x^3+15x^4+21x^5+...?

    Homework Statement Find the closed form of the following power series 1+3x+6x^2+10x^3+15x^4+21x^5+... Homework Equations 1+x+x^2+.. = 1/(1-x) The Attempt at a Solution I tried differentiating but couldn't get it to any expression that I know the sum for.. I was playing around...
  4. H

    Closed subset (with respect to weak topology)?

    Let LG be the base point preserving loops (it's a Hilbert manifold). So LG = { f : S^1 -> G s.t. f(0)=1 } where G is a connected, simply connected Lie group. LG is embedded into the (vector space) Hilbert space L^2[0, 2pi] given by f |--> g(t) = f '(t)f(t)^-1 Is LG a closed subset of...
  5. K

    Identifying if A is Open or Closed

    Homework Statement For the following set, state and justify whether or not it is open or closed. Homework Equations A={z| I am z >1} The Attempt at a Solution I know the definition of an open set, but I am not sure how to use it to solve this question.
  6. 2

    Could a Collapsing Universe Result in a Cosmological Blueshift?

    If the Universe stopped expansion 10 million years ago and started to collapse Whould it their be such a thing as cosmological blueshift? Would the scalefactor-redshift be R=1/(z - 1) or R=1/(1+z)? I think since universe is collapsing then spectra will be blueshifted! The scale...
  7. M

    Engineering Signal reflections in open and closed circuits

    I'll try to make this as concise as possible. I'm trying to get my head around how signals behave in coaxial cables. If you set up a circuit like this: Then the earthed end will force a node at that end, right? So you'll end up with your reflections having a phase shift of pi and looking...
  8. F

    Understanding Open and Closed Sets: Defining and Recognizing |z|<2

    Homework Statement For the following set state and justify: i) whether or not it is open? ii) whether or not it is closed? {z||z|<2} Homework Equations The Attempt at a Solution I really don't know where to start on this question, i don't understand this topic at...
  9. D

    Two Closed Thermodynamic Cycles Conceptual Question

    Imagine processing the gas clockwise through Cycle 1 and then counterclockwise through Cycle 1. Compare these two processes on the basis of the heat energy transferred to the gas in the entire cycle. Choose the correct comparison symbol. Q_clockwise for Cycle 1 <,=,> Q_counterclockwise for...
  10. G

    What Does 'Closed Under Addition' Mean in Mathematics?

    What does it means by closed under addition For eg : As S is closed under addition S = {gn : n is a member of integers} could anyone elaborate more on this and gimme some example ? Does it mean that when something is closed under addition , we only consider addition and nothing else ?
  11. H

    Is there a smallest closed ball containing a closed set in a metric space?

    I was reading about the Nested sphere theorem and a thought occurred. if you have a sequence of decreasing closed sets whose diameter goes to zero in the limit, we can show that the intersection of all these sets is a single point. my idea was to show this using nested sphere theorem if we...
  12. R

    Understanding He Closed Cycle Cryos and Vibration Damping

    Hi All, I need some basic info of He closed cycle cryos..(like working principle, etc).. I have a compressor, which compress He gas and passed into a cryo's coldhead. So He gas expands in side the coldhead and cools the coldhead..then it again passes into compressor..so the cycle repeats.. I...
  13. B

    Understanding Closed Neutron Shells: Determining the Elements with Stable Nuclei

    Homework Statement which of the following has closed neutron shells? (the number in front should be a superscript) 36S, 50V, 50Ca, and there are more but i just want to understand why. Homework Equations The Attempt at a Solution i know the answers, i just don't know how to get...
  14. I

    Need help understanding sceanario only, is it a closed reversible system?

    Homework Statement @= alpha= thermal expansion coefficent= 5.1x10^-5 Kt= compression= 3.2x10^-5 B=beta= -(dE/dV)t = 0.5 Po=1 atm To=293K Vo=1L ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Solid held in a piston and cylinder at equilibrium is in a constant temperature bath at 293k. Two...
  15. P

    Perforated Pipe Flow with a closed end

    1. A hydroponic garden uses the 10 m long perforated pipe system to deliver water at 20ºC. The pipe is 5cm in diameter and contains a circular hole every 20 cm. A pump delivers water at 75 kPa (gage) at the entrance, while the other end of the pipe is closed. pressure near the closed end of the...
  16. V

    How Long Should an Organ Pipe Be to Resonate at 16.4 Hz?

    Homework Statement The Lowest note on an organ is 16.4 Hz. a. What is the shortest pen organ that will resonate at this frequency b. What is the pitch of the same organ pipe is closed Homework Equations f=V(n)/2L, n=1,2,3.. f=V(n)/4L, n-1,3,5... The Attempt at a Solution I understand...
  17. R

    Is K Open or Closed? A Topology GRE Question

    I'm not very good at topology but am reviewing it for the GRE Subject Test. Here's a question that I think I know, but would like to check with you guys. We define: Ek = B(0, k) - B(0, k-1), where B(0,k) is an open ball around the origin with diameter k. Now suppose that Tk is a subset of Ek...
  18. A

    Properties in a closed system Help

    Properties in a closed system...Help! Homework Statement A cylinder, locked by a plug, contains 1kg of 'wet' steam at a pressure of 5 bar (state point 1). In the locked position, heat is added through the wall of cylinder into the wet steam until the mixtures become dry saturated at 200...
  19. J

    Is the magnetic induction line closed

    It is said that every magnetic induction line is closed.but recently I happended to find one which isn't. Consider the magnetic field generated by a ring form circuit, the magnetic induction line which I have found is not closed is the one that go through the center of the circuit,which is...
  20. C

    Comparison of FEA and closed form solution for fluid velocity in a channel

    I am trying to compare the fluid velocity given by the closed form solution and FEA analysis for fluid flowing through a channel that is 800u long and 100u wide. I am using the equation vmax= (gradP)*(radius)^2/(4*viscosity) I got 8.4cm/s in the former compared to ~10cm/s in the latter...
  21. O

    Prove that if C and D are closed sets, then C U D is a closed set.

    Homework Statement I want to show that if C and D and closed sets, then C \bigcup D is a closed set. Homework Equations A set is called closed iff the set contains all of its accumulation points. The Attempt at a Solution In order for me to prove this statement, I will be able...
  22. I

    Analysis: Closed sets and extrema

    Homework Statement a) Let U be a closed subset of the reals with an upper bound. You know that U has a supremum, say z. Prove that z is an element of U. b) Suppose U is a closed subset of the real numbers with an upper and lower bound. Prove that U has a maximum and minimum.The Attempt at a...
  23. B

    Asymptotic approximation to a closed contour integral

    Find an asymptotic approximation as p goes to infinity: f_{\lambda}(p)=\oint_{C}exp(-ipsinz+i\lambda z)dz where C is a square contour and p, lambda are real. Taking C to be of side length pi and centered at the origin, I applied the method of steepest descent at the point z=-pi/2...
  24. C

    Why is the amplitude maximum at the open end of a closed and open end tube?

    Consider a scenario of a sound wave inside a closed end and opened end tube. We always learn that the displacement amplitude at the closed end is always zero but at the opened end is always maximum. My friend can see it quite intuitively. For the closed end, we expect there is no...
  25. E

    Advanced Calc 1 Question about Closed Sets

    Homework Statement Suppose f: [a,b] -> R and g: [a,b] -> R are both continuous. Let T = {x: f(x)=g(x)}. Prove that T is closed. Homework Equations If a function f: D -> R is continuous, then for each E > 0 there exists a delta >0 such that if |x-x0| < delta (for x, x0 in D) then...
  26. W

    Divergence-free field has closed field lines?

    Is the restriction that a field is divergence-free enough to ensure the field lines will be closed? How can one (dis-) prove such a statement?
  27. U

    Function that is open but not closed?

    Homework Statement An example of a function that is open but not closed, and an example of a function that is closed but not open. Homework Equations The function f is open (closed) if f[A] is open (closed) for each open (closed) set A in X. The Attempt at a Solution This is a...
  28. B

    Closed End Tubes: Length, End Correction & Resonance

    I been doing a lot of research on this subject and have learned a great deal, but there are a few details I need some answers on. From what I have read, you can have a wrong length of closed end tube, and you will need to tune it by means of a sliding collar, stopper, or coning the mouth. So, if...
  29. D

    What is the relationship between a closed set and a converging sequence?

    Homework Statement http://img527.imageshack.us/img527/6049/48193240ao5.png I don't understand this proof. The first two lines are clear to me: the sequence xn is in F and F is closed so its complement is open so there is a ball with radius r around x in Fc. But I don't understand the last...
  30. Topher925

    Is the universe an open or a closed system?

    I recently was having a discussion about entropy and the concept of the universe being an open or closed system came up. Assuming that the universe is infinite, would it be considered to be an open or a closed system? A closed system being a system in the state of being isolated from the...
  31. S

    Thermodynamics: Addition of saturated steam to closed tank

    Homework Statement A well-insulated closed tank is of volume 70 m^3. Initially, it contains 25000 kg of water distributed between liquid and vapor phases at 30 deg C. Saturated steam at 11 bar is admitted to the tank until pressure reaches 7 bar. What mass of steam is added? Homework...
  32. G

    Current decay in closed circuit with only 1 resistor

    Hi this is my first post so please be nice :) 1. Homework Statement The problem has been set up that a circuit containing a resistor and switch is being driven by a power source of unkown potential. The switch is flick to short the power source leaving only the resistor in a closed loop...
  33. S

    Are These Sets of Matrices Closed Under Multiplication?

    A set S of (necessarily square) matrices is said to be closed under multiplication if AB∈ S whenever A, B ∈ S. Which of these matrices are closed under multiplication? Circulant matrices Upper triangular matrices Hessenberg matrices My trouble: How do I go about figuring this one out?
  34. C

    What Are Closed Timelike Curves?

    i was going over some relativity search online and came across what is called a closed timelike curve and that i actually allows time travel, am i right?
  35. F

    Exploring Conservation Laws in Closed Systems

    In classical mechanics (also in QM I guess), the fundamental laws of conservation (energy, momentum and angular momentum. tell me if I forget something) are valid only if the system is closed and the net external force is zero. WE define what the system is. We can include or exclude things...
  36. B

    Two beakers with volatile solvents in closed system

    Homework Statement Beaker A contains a volatile solvent and beaker B contains 10% solution of a non-volatile solute in the same solvent. Both beakers are placed in a closed environment as shown. The question asks what will happen when the system has reached equilibrium. The answer is given...
  37. B

    Can the Extreme Value Theorem Apply to Function f on Interval [-3, 5]?

    1. The problem: The function f is continuous for -3\leqc\leq5 and differentiable for -3<x<5. If f(-3)=6 and f(5)=-2, which of the following could be false? (a) there exists c, where -3\leqc\leq5, such that f(c)\geqf(x) for all on the closed interval -3\leqx\leq5. (b) There exists c, where...
  38. T

    Do Closed Timelike Curves Exist?

    im doing my project for school on this a need help.
  39. B

    How can I put this summation into a closed form?

    Hi, I can't think / remeber how to write the following expresion in a closed form, the function is a summation of natural numbers between 1 and an upper limit "K", written as Sigma x with limits K and 1 effectivly, straightforward etc... what i want is the summation of all the...
  40. S

    Open and Closed Pipe Length for Harmonics

    Homework Statement a pipe in air at 20 degrees celsius ia to be designed to produce two succesive harmonics at 240Hz & 280Hz. how long must the pipe be, and is it open or closed? Homework Equations v=\lambdaf The Attempt at a Solution sorry, i could not do it. i totally can't...
  41. NightSwimmer

    Question regarding air flow in a closed circuit

    I am new to this forum. I am an applications engineer. I design, build and program industrial automated control systems. I am currently working on a project for a lime calcining kiln. Our project involves an upgrade of the coal-fired kiln's fuel delivery system. This involves a coal grinding...
  42. D

    Electric flux through closed surface

    Homework Statement Find the total electric flux through the closed surface defined by p = 0.26, z = \pm 0.26 due to a point charge of 60\mu C located at the origin. Note that in this question, p is defined to be what r is defined conventionally, and \phi takes the place of \theta. This is...
  43. I

    Is the Set M Closed in the Space X?

    Homework Statement Let X=(C([0,1]), || . ||_1 ), where ||f||_1=\int_{0}^{1}|f(t)|dt. Let M=\{f \in C([0,1]) : \int_{0}^{1}f(t)dt=2, f(1)=0\}. Is M closed in X? The Attempt at a Solution I've tried the following: Let f_n be a sequence in M such that f_n \rightarrow f. I'm checking whether f...
  44. S

    Set of cluster points being closed

    Homework Statement (X,d) metric space, we have a sequence xn from n=1 to infinity G is a subset of X containing all cluster points of sequence xn. need to show that G is closed. The Attempt at a Solution I tried to show that X\G is open. so take any point c in X\G, there exists an...
  45. M

    What is the Difference Between an Open and Closed Universe?

    Hello, I'm not sur if this is the right section. Please could a mod move it if it isn't. I've only just got into physics and so i don't want anything tooo complicated Could someone please explain the difference between an open and closed univers Thanks _Muddy_
  46. T

    Boiling liquid in a closed vessel

    Hi dear Forumers, I 've run into a little thermodynamic problem: There is a closed vessel, containing a given amount of liquid. I heat up the vessel, higher than the boiling point of the liquid. Here it is what happens: As a start, I know that the pressure inside the vessel consists of...
  47. C

    Entropy Equatio for a closed system

    I must have already been banned for spamming threads. But oh well. You know how change in entropy dS of a closed system assuming reversibility of the processes = (\frac{dQ}{T})_{rev}=\frac{C_{p}dT}{T} So when you try to find the actual entropy with respect to temperature, it's: \displaystyle...
  48. X

    Contains closed set Accumulation points?

    Homework Statement Hello, I am here a novice and my English is very bad. I am a student and now we learning about sets. I have got a problem, how to proof, that every closed set contains all accumulation points? I know / hope, that should, but I want to proof it. I hope, that somebody will...
  49. S

    Really basic what happens when the switch closed question

    Hello guys, I got a small question. It says circuit consists of three identical lamps connected to a battery with a switch as shown in the diagram. When the switch is closed what happens. I did this really quick on paint. w_w_w_.hotlinkfiles.com/files/1210467_pxtdw/untitled.JPG they are not...
  50. B

    Understanding Closed Feedwater Heaters and Regeneration in the Rankine Cycle

    I have a question on the rankine cycle with a closed feedwater heater. My thermo book says that in an ideal closed feedwater heater, the feedwater is heated to the exit temperature of the extracted steam. I don't really understand this. I know the bleed steam from the turbine is cooled to a...
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