Closed Definition and 1000 Threads

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...

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...

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...

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_

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...

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...

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...

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...

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...

Homework Statement Once closed organ pipe has a length of 3.2 m. Frequency of the note played by this pipe is 27 Hz. When a second pipe is played at the same time, a 1.50 Hz beat note is heard. By how much is the second pipe too long? Homework Equations ? The Attempt at a Solution...

Homework Statement A mapping f from a metric space X to another metric space Y is continuous if and only if f^{-1}(V) is closed (open) for every closed (open) V in Y. Use this and the metric space (X,d), where X=C[0,1] (continuous functions on the interval [0,1]) with the metric d(f,g)=\sup...

[SOLVED] Show subspace of H^1[0,1] is closed Homework Statement I have an assignment that deals with some Sobolev spaces but I have never worked with them before. Only the definitions are given. Consider the Sobolev space W^{1,2}([0,1])=H^1([0,1])=\{u\in C([0,1]): \mbox{ there exists }...

[SOLVED] Finding the Max Value of a Function on a closed interval Homework Statement Hi, I'm reposting this because it's a subsection to a larger question I had and I figured more people might be able to help with a new topic name. anyway i have the equation (eq1) C(t) = C + a(e^.5t) +...

Hi For our control systems project, we are trying to implement a closed feedback image focusing system. A digital camera captures the image of an object (a checkerboard), sends it to a computer algorithm which determines the amount of defocus in it and sends an actuation signal to a stepper...

We have two closed sets A,B in R^n. Does A+B= {x+y | x is an element of A, y is an element of B} have to be closed? I know that both the union and intersection of two closed sets have to be closed. I'm guessing from the question that the answer is no, but I've been playing around with different...

Let A, B in R^n be closed sets. Does A+B = {x+y| x in A and y in B} have to be closed? Here is what I've tried. Let x be in A^c and y in B^c which are both open since A & B are closed. So for each x in A^c there exists epsilon(a)>0 s.t. x in D(x, epsilon(a) is subset of A^c. For each y...

[SOLVED] Topological Properties of Closed Sets in the Complex Plane Homework Statement 1. Show that the boundary of any set D is itself a closed set. 2. Show that if D is a set and E is a closed set containing D, then E must contain the boundary of D. 3. Let C be a bounded closed convex set...

Would it be possible for someone to check over my experiment? I have not conducted the experiment yet, but I would like to make sure I am on the right tracks. The equation I will be using to determine the speed of sound is: v=f\lambda v is the speed of sound f is the frequency and this will...

Homework Statement Let (X,d) be a metric space. Can a set E in X be both open and closed? Can a point in E be both isolated and an interior point? Homework Equations I've used the metric defined as d(x,y)=1 for x\ne y and 0 if x=y (we used this in a previous problem). I also used the...

Hi Friends, We are stuck between two scenarios here on a closed loop shade system we are putting together. First, the way this system works is there is a roller containing a shade panel wrapped around it (just like a window shade) and the shade panel connects to a hem bar. Then a steel cord...

If you vibrate a tuning fork over a closed pipe (a pipe with one end closed and the other open) is it possible to get overtones in the pipe even thought the tuning fork only vibrates at one frequency For example if you have a tuning fork of freq 300HZ and you allow it too vibrate above a closed...

an experiment^^ in a closed container, means tat it has a constant volume. when i increase the air pressure inside(without heating), the result is the temperature will increase. why? can i hav a theoretical explanation? thx for reading

Homework Statement The Premise: Here One must prove that that R^n and Ø are the two subsets of R^n, which is both open and closed. You must that these are the only subsets of R^n which has this property! Let X \subseteq \mathbb{R}^n be a subset, which is both open and close, and here...

What would be an example of two closed subspaces of a normed (or Banach) space whose sum A+B = {a+b: a in A, b in B} is not closed? I suppose we would have to look in infinite dimensional space to find our example, because this is hard to imagine in R^n!

Homework Statement How is the theorem "Continuous functions have closed graphs" proven in the setting of a general topological space? (assuming the theorem is still valid?)

[SOLVED] Closed real vector spaces Homework Statement Determine whether the given set V is closed under the operations (+) and (.): V is the set of all ordered pairs of real numbers (x,y) where x>0 and y>0: (x,y)(+)(x',y') = (x+x',y+y') and c(.)(x,y) = (cx,cy), where c is a...

[SOLVED] Closed Environment Sound at Light I had an idea regarding sound at light speed. If you are in a closed box and are traveling at the speed of light and you flick your finger, since the oxygen is also traveling at the speed of light would it make a sound relative to your position. If so...

Can anybody suggest how to write an open interval (a,b) as a combination(union, intersection and compliment) of closed intervals of the form [c,d] and vice versa. What if closed intervals are half closed as following (-inf, f]. 'f' being rational.

Hi to all What exactly is the difference between Banach(=complete, as far as I understand) (sub)space and closed (sub)space. Is there a normed vector space that is complete but not closed or normed vectore space that is closed but not complete? Thanks in advance for explanation and/or examples.

What would be an example of a not (topologically) closed subspace of a normed space?

Why a magnetic flux in closed surface area is always 0?

Homework Statement I am looking for a closed form of the summation: sin(x) + sin(3x) + sin(5x) + ... + sin((2n-1*)x) Homework Equations None. The Attempt at a Solution Through a complete stroke of luck, I believe I have arrived at the correct solution: sin^2(nx)/sin(x) I have...

Ok, the proof looks simple since by defintion Cl A = intersection of all closed sets containing A. And textbooks give a quick proof that we all understand, but I have a question: Don't we first have to prove that a smallest closed set containing A exists in the first place? I'm trying to...

1. If set A is compact, show that f(A) is compact. Is the converse true? 2. If set A is connected, show that f(A) is connected. Is the converse true? 3. If set B is closed, show that B inverse is closed. Any help with any or all of these three would be greatly appreciated. Stumped!

1. If A is compact, show that f(A) is compact. Is the converse true? 2. If A is connected, show that f(A) is connected. Is the converse true? 3. If B is closed, show that B inverse is closed. Any help with any or all of these three would be greatly appreciated.

Homework Statement Let X be a topological space. Let A be compact in X. Let B be contained in A. Let B also be closed in X. Is it always true that B is compact in X? Homework Equations The Attempt at a Solution

Homework Statement the max value of f(x)=x^3(40-x^2) on the closed interval 0<= x <= 40 occurs at x=? The Attempt at a Solution different problem, same story (notes are unclear, and the book only complicates things more). I know the answer is 24, but this will not help me on the final exam...

Why is a sealed pop bottle said to be in a state of equilibrium, while an opened bottle is not?

Homework Statement I have a closed set in an open set in a metric space and I am trying to find an epsilon radius of the closed set that is in the open set. So I want to find some way to take the infimal distance between the boundary of the closed set and the boundary of the open set...but I...

For less than BH_h, deep in gravitational potential well, with very extreme curvature, might one have a future light cone tipping over sufficiently to become spacelike and then wrap around to join up (glued) to past light cone? This is like a closed timelike curve, which can not be shrunk to a...

I have a question: I understand why the expansion of the universe is believed to be caused by the expansion of vacuum space, i.e. the Hubble flow. I understand that if the universe had mass/energy in excess of its critical density, then it would be a "closed" universe which would...

Homework Statement An 80-cm long air column, closed at one end, contains sounding waves. How long is the wavelength that corresponds to: the first overtune Homework Equations v = f(lambda) The Attempt at a Solution no clue about what to do.

Homework Statement I'm looking to find a closed form for the infinite series: 1*C(n,1) + 2*C(n,2) + 3*C(n,3) + ... + n*C(n,n) Homework Equations C(n,k) = n!/(k!*(n-k)!) C(n,1) + C(n,2) + C(n,3) + ... + C(n,n) = 2^n - 1 The Attempt at a Solution I'm not quite sure where to start...

Homework Statement I am trying to find the probability that a valve will be able to undergo one cycle of demand? Given that a particular type of remotely controlled mechanical valve can be assumed to have a probability of not opening, when closed, of 0.02 and a probability of not closing...

Homework Statement This is a topology problem. I have a continuous map from X to Y, and I take an open set U in Y, and I look at its preimage. Is it true that there must always be an open set in X whose closure is in the preimage of U? I know that there is always an open set whose closure is...

The question asks to prove directly that the closed interval is covering compact - U= an open covering of the closed set [a,b] I started by taking C=the set of elements in the interval that finitely many members of U cover. Now I need to somehow use the least upper bound theorem to show...

Infinite Sum [n=1] 1/Fibonacci[n] Or this, Infinite Sum[n=1] 1/(n^n) Using some known mathematical constants.

Homework Statement The question I'm working on is First the diagram:http://http://i215.photobucket.com/albums/cc10/Spookie71/image0-12.jpg There is the matter of the equation I use to solve the equation: Can you please explain for me? Scott

Homework Statement Check to see if the (vector space) set of rational numbers is closed under addition and scalar multiplication Homework Equations The book says this holds for addition but fails for scalar multiplication. The Attempt at a Solution Im a little confused. You can...

Is there a theoretical limit to the lowest note achievable in a closed tube(Pop bottle)? Heres the question in context: I've got what I believe to be the correct: http://img141.imageshack.us/img141/9301/1azw1.jpg ^^ May want to check that, if you don't mind ^^