Closed Definition and 1000 Threads

Hi, Everyone: I have a quadratic form q, defined on Z⁴ , and I know the value of q on each of the four basis vectors ( I know q is not linear, and there is a sort of "correction" for non-bilinearity between basis elements , whose values --on all pairs (a,b) of...

Hi All, I've come across a theorem that I'm trying to prove, which states that: The quotient group G/H is a discrete group iff the normal subgroup H is open. In fact I'm only really interested in the direction H open implies G/H discrete.. To a lesser extent I'm also interested in the H...

I would like a second opinion on my answer to this question as I'm confusing myself thinking about my proof. Any input is appreciated Homework Statement "Let (X, ||.||) be a complete normed linear space and Y \subsetX be a non-empty subspace of X. Then (Y, ||.||) is a normed linear...

So I am reading a text written by my Thermodinamics professor and I find something that I still can't accept. "(Sistema fechado) É aquele que não troca massa. (...) Um sistema fechado é dito isolado quando não troca energia. Entretanto, essa definição de sistema não é consistente com a teoria...

Hey guys, i just started taking a course on ST and so far we discuss the closed string following Green, Schwarz, Witten. I don't see the point of constructing the Virasoro algebra (formula 2.1.85 in GSW) if the corresponding generators are zero due to the constraints. Or to put it differently...

I need help understanding this conceptually, so can anybody please correct me and help me understand this? If I'm correct then just say so.Diagram: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/labVpic3.jpg the circles are bulbsOk so the basically in an open circuit there is no flow and...

Homework Statement (X,d) is a metric space B(x) is the set of all bounded functions on X show that f = {g \in B(X) g is continious} is a closed subsetThe Attempt at a Solution A hint of how to start?

I can't seem to find an equation that fits the situation I am facing. Either that, or I just don't believe the answer the current equations are providing. I am trying to develop the size for an air compressor to fill up a train braking sytem. I have equations for most of the system, but I...

I have a question about the Remark on the page posted. When it says "If γ and all its derivatives take the same value at a and b, there is a unique way to extend γ to a (b − a)-periodic (smooth) curve γ : R → R^n" what does this exactly mean? I suppose that the condition that the derivatives...

Homework Statement In a lab that we performed, we had a closed tube with piezo electric transducers on both ends, and they were attached to a frequency generator. We found the frequencies that caused resonance, and the lab wants us to calculate the velocity of the wave using data. The lab...

Homework Statement a) Determine what the thickness should be in a closed tube versus an open tube to have the same twist angle b) Determine what the thickness should be in a closed tube versus an open tube to have the same max shear stress G=20GPa T=50Nm tr=1mm (for the open tube)...

Say, all objects in a closed Universe are neutral, and there is only 1 (unbalanced) positive charge. Lines of an electric field started on a positive charge can end only on the negative charge or they go into infinity. But in a closed universe there are no negative charges nor they can go...

Standing waves have a fundamental frequency equal to 4x the length of the pipe if the pipe is closed at one end and open at the other end. So, blowing across the top of a 33.2 cm bottle should produce a fundamental frequency of v/4L or about 340/1.2= 283 hz. When I record the sound produced...

Hello, I am having trouble finding an example of a set in R^2 that is neither open nor closed. I have already shown the half open interval [0,1) is neither open nor closed, but I can't seem to find any other examples. Can someone push me in the right direction? Would x^2+ y^2<1 be open nor...

The 2nd law of thermodynamics refers to closed systems. 1. If we imagine a universe of infinite extent but where only one object exists that emits e/m waves, is that a closed system? 2. If we imagine a universe where only two asteroids exist and are orbiting each other, and a machine between...

Prove that the intersection of any collection of closed sets in a topological space X is closed. Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Let r be a positive number and define F = {u in R^n | ||u|| <= r}. Use the Componentwise Convergence Criterion to prove F is closed.Homework Equations The Componentwise Convergence Criterion states: If {uk} in F converges to c, then pi(uk) converges to pi(c). That is, the...

A set S is closed iff it contains all its adherent points iff it contains all its accumulation point? From what I know, in general accumulation point is a subset of adherent point, but if supposed I have a closed set, then the "if and only if" forces me to conclude that accumulation point =...

Homework Statement A closed surface with dimensions a = b = 0.254 m and c = 0.4064 m is located as in the figure. The electric field throughout the region is nonuniform and given by ~E = (α + β x^2)ˆı where x is in meters, α = 4 N/C, and β = 6 N/(C m2). Picture of object attached...

Im looking for a way to create solar heat activated condensation..Possibly a sodium acetate or zeolite/water system..A hot/Cold heat pump system generated only by heat and night time cooling to create a dehumidity effect..Basically create water from air with a chemical in a closed loop system.Is...

Let E be the vector space of bounded functions f:N --> R, with the norm(g) = sup|f|. Assume without proof that the norm holds, so that the function d(f,g)=norm(f - g) is a metric. Prove that the vector subspace F={f in F | f(n) -->0 as n --> infinity} is closed in E. Here is what I have...

Hi, I'm new to Physics Forum and wasn't really sure where to post this since its not strictly speaking a homwork question. So if it happens to be in the wrong place I apologise. I was looking through some lecture notes from when I did my Physics degree years ago and come across a problem...

Homework Statement Let Y be a subset of X. Give an example where a set A is closed in Y but not closed in X. Homework Equations A set is closed if its complement is open. A set is open if for every element x0 of the set, there exists an E > 0 such that U(x0;E) = {x|d(x,x0)< E} is...

Homework Statement For each w \in \mathbb{C} define the function \phi_w on the open set \mathbb{C}\backslash \{\bar{w}^{-1}\} by \phi_w (z) = \frac{w - z}{1 - \bar{w}z}, for z \in \mathbb{C}\backslash \{\bar{w}^{-1}\} \back. Prove that \phi_w : \bar{D} \mapsto \bar{D} is a...

Hi everyone, I'm reading Rudin's Analysis and in the topology section, he implies that the finite intersection of closed sets is not necessarily closed. (pg. 34) Can someone give an example of this? I can't seem to find one.

Homework Statement Is it possible for a flute (tube open at both ends) 72 cm long and an oboe (tube open at one end) 64.8 cm long to produce the same note? Prove your answer. Homework Equations v=f\lambda L=(n/2)\lambda (tube open at both ends) L=((2n-1)/4)\lambda (tube open at...

Hi All, I have been battling with this question for a while. Given a conservative vector field, we know that there are infinitely many closed paths where the line integral evaluated is zero. In fact this is the requirement for a conservative vector field: Every line integral of any closed...

Homework Statement I'm looking for a closed form expression for the partition function Z using the Canonical Ensemble Homework Equations epsilon_j - epsilon_j-1 = delta e Z = Sum notation(j=0...N) e^(-beta*j*delta e) beta = 1/(k_B*T) t = (k_B*T)/delta e N is the number of excited...

Homework Statement 31.47mol of copper at 273 kelvin put inside an isolated cup along with 1 mol of water vapors at 373 Kelvin. (pressure is constant at 1 atm). ALL of the water condensed. given parameters: Cp(Cu(solid)) = 24.44 J/mol Cp(H20(gas) = 33.58 J/mol Cp(H20(liquid) = 73.35...

Homework Statement Let X be the integers with metric p(m,n)=1, except that p(n,n)=0. Show X is closed and bounded but not compact. Homework Equations I already check the metric requirement. The Attempt at a Solution I still haven't got any clue yet. Can anyone help me out?

Homework Statement Given the set S = the intersection of the rationals and the interval [0, 1], is S open or closed? Homework Equations Definition of open: for all elements of S, there exists epsilon > 0 such that the neighborhood (x, delta) is a subset of S. The Attempt at a Solution...

[b]1. Prove that a set is closed if and only if it contains all of its cluster points. [b]2. Can I use part of the Lemma here that states: Every interior point of A is a Cluster point. Also what exactly is the definition of a closed set other than a set is closed if its compliment is...

Hi, everyone, I need some help with the following: Homework Statement Given is, that the following power series: \sum_{n=0}^{\infty} \frac{x^{3n}}{(3n)!} is the solution to the following differential equation: y''' - y = 0. Find the closed form of the series. Homework Equations...

consider a real function f(x) where x\in[a,b] Why f'(x),\; x\in(a,b)

Homework Statement Suppose [a,b] is a closed interval (on R), and {xn}n>=1 is a sequence such that a) xn belongs to [a,b] b) lim as n--> infinity xn = x exists prove x belongs to [a,b] Homework Equations The Attempt at a Solution Well since any sequence is bounded, then...

Is every orientation form w on a compact smooth manifold closed?(i.e. dw=0)

What is the value of a surface integral over a closed, continuous surface of a vector field of vectors normal to the surface? The integral of ndS over S. I believe the answer is zero. Can someone direct me to a proof for an aribitrary closed surface?

Given my limited background in Physics, I am restricted to the popular literature on M-theory. After going through this literature (including articles from the very helpful "annotated list of useful literature for String Theory" posted in this rubric of the Forum), I am still puzzled by the...

Forgive me because I'm not a math or physics wiz but I'm at a dead end trying to calculate the pressure generated by a deflagration inside a cylinder. I have been searching for a formula but I've come up with nothing. Here is an example scenario: I have a cylinder with a height of 9cm and...

Mass can curve space-time. Is it possible that space-time around a black hole is so badly curved that it forms a closed 4D manifold?

Homework Statement Prove that a point,a, not belonging to the closed set B has a non-zero distance from B. I.e that dist(a,B)=inf(y in a) ||a-y||>0 Homework Equations I have no idea how to start this. It is only worth a few marks and I have been told it is fairly easy but I have always...

Help me Understand "Closed Under Addition" and "Closed Under Multiplication" Linear Algebra...matrices...etc Examples would be great. Thanks.

Homework Statement Here's a nice one. I hope it's correct. Let p : X --> Y be a closed, continuous and surjective map such that p^-1({y}) is compact for every y in Y. If X is Hausdorff, so is Y. The Attempt at a Solution Let y1 and y2 in Y. p^-1({y1}) are then p^-1({y2}) disjoint...

Homework Statement Let p : X --> Y be a closed, continuous and surjective map. Show that if X is normal, so is Y. The Attempt at a Solution I used the following lemma: X is normal iff given a closed set A and open set U containing A, there is an open set V containing A and whose...

So I have to show that a projection P (i.e a linear operator with P=P²) on a Banach space X is bounded if and only if \ker (P) and P(X) are closed subspaces of X.My idea was to boil it down, using the closed graph theorem. What's left for me now is to show that the graph G(P):=\{(x,y)\in X\times...

I've been studying the behaviour of speakers and headphones for my own interest. I was able to derive the differential equation governing the motion of the speaker itself, what I've had trouble doing is deriving the pressure created by the speaker. First the equation I've derived for...

Homework Statement As the title says, one needs to show that if A is a closed subspace of a Lindelöf space X, then A is itself Lindelöf. The Attempt at a Solution Let U be an open covering for the subspace A. (An open covering for a set S is a collection of open sets whose union equals...

EDITED: I decided to move the thought experiment that led me to this question to the bottom of this thread. I will first state what my question is. Suppose that we live in a closed universe of three spatial dimensions and this universe is in a state of rapid collapse. Now suppose that all of...

Homework Statement I basically have a closed loop of wire with a current flowing through it clockwise. I need to determine the magnetic field in the center, along the z-axis. Homework Equations Ampere's Law and Biot-Savart Law The Attempt at a Solution Using Biot-Savart Law I...

Homework Statement How to define closed,, open and compact sets?Are they bounded or not? Homework Equations For example {x,y:1<x<2} The Attempt at a Solution It's is opened as all points are inner Can you please say the rule for defining the type of the set? Like for example...