Closed Definition and 1000 Threads

This is problem 4.7.11 of O'Neill's *Elementary Differential Geometry*, second edition. The hint says to use the Hausdorff axiom ("Distinct points have distinct neighborhoods") and the results of fact that a finite intersection of neighborhoods of p is again a neighborhood of p. Here is my...

Show that every closed set in R has a countable dense subset. Let's call the set F. I've been thinking about this problem for a little bit, and it just doesn't seem like I have enough initial information! I tried listing some things that I know about closed sets in R: $\cdot$ Countable...

Homework Statement I have a metric for wormhole. Now if I want to find the closed trajectory for this metric how will I proceed from here? Help me with detailed maths if possible. Homework EquationsThe Attempt at a Solution

Some exact solutions to Einstein's General Relativity show that Closed Time like Curves may theoretically exist. Could they actually exist in our universe? And if so, how would it change the understanding of physics and our universe?

Homework Statement The first exercise in Susskind and Hrabovsky's The Theoretical Minimum is one that, in the words of Susskind, "is designed to make you think, more than it is designed to test you." The exercise asks: Homework Equations In the prior paragraph, the authors define the notion...

Homework Statement A closed organ pipe of length 1.00m is filled with a gas and is found to give the same note as an open pipe of length 1.30m filled with air, when both are resonating at their fundamental mode of vibration a) draw diagrams to show the nature of the waves in each pipe and use...

Homework Statement https://pasteboard.co/Hj3g5Km.jpg When both switches 1 and 2 are closed,what is the total resistance of the set up? I couldn't figure out which resistors are connected in parallel and which resistors are actually in series in this set up when both swtiches are closed. I...

How may we go about to show that, $$\int_{0}^{1}t\cos(2t\pi)\tan(t\pi)\ln[\sin(t\pi)]\mathrm dt=\color{green}{1\over \pi}\cdot\color{blue}{{\ln 2\over 2}(1-\ln 2)}$$

Homework Statement There is a system of 4 points located along a circle of radius R. Points are connected by undeformable ropes (pink on the picture). There is a force applied to each point. Scheme: https://we.tl/MsCEViCQdB I need to find resulting force in the system. The Attempt at a...

Proposed: How can we prove $(1)?$ $$\int_{0}^{\infty}\mathrm dx{\sin^2\left({a\over x}\right)\over (4a^2+x^2)^2}={\pi\over (4a)^3}\tag1$$

I have been trying to find an answer to this problem for some time. So I was hoping the community might be able to point me in the right direct. https://drive.google.com/open?id=1Y2hYkRG94whLroK20Zmce07jslyRL3zZ I couldn't get the image to load. So above is a link to an image of the problem...

I'd like to integrate a function over a closed circle-like contour around an arbitrary point on a torus and I assume I would use the expression: $$ \int_{t_1}^{t_2} f(x,y,z) \sqrt{x'(t)^2+y'(t)^2+z'(t)^2}dt$$ And I cannot come up with an explicit parameterization of the variables in terms of...

Dears Kindly, I want to hear from you regarding this topic. The system is closed cooling system. I believe it is difficult to attribute the sound you hear from centrifugal pump to be a cavitation especially if the discharge pressure is normal. The last time we had a problem with this system...

Hi, I am confused about the electric field lines which are depicted mostly on the Internet as per conventional way. What I understand that the conventional current was due to positive charges which was wrong. Actual flow of the current was due to the negative charges or electrons. When the...

Homework Statement "Let ##E \subset ℝ##. Prove that ##E## is closed if for each ##x_0##, there exists a sequence of ##x_n \in E## that converges to ##x_0##, it is true that ##x_0\in E##. In other words, prove that ##E## is closed if it contains every limit of sequences for each of its...

I have a long steel uninsulated cylinder filled with hydraulic fluid (let's say it's mineral oil), and I need to figure out how many barrel heaters to clamp onto it in the winter months to prevent the steel surface temperature from dropping under 40 degrees Fahrenheit. My question is, how do I...

I am reading about this most famous experiment in physics, the double-slit experiment. My question is very simple: in the "Delayed Choice" version, have they done the test where they close BOTH SLITS (at once) after the photon has passed the slits?? If so, what have been the result? Can you...

I believe the electric flux within a closed space can be found with the equation phi = Q/ε0. Can this be used for volume and area, or just volume? Also what good does this do. Why would I want to know the electric flux of something?

The Brian Hall's book reads: A Lie group is any subgroup G of GL(n,C) with the following property: If Am is a secuence of matrices in G, and Am converges to some matrix A then either A belongs to G, or A is not invertible. Then He concludes G is closed en GL(n,C), ¿How can this be possible, if...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with another aspect of the proof of Proposition 1.2.17 ... ... Duistermaat and Kolk's Proposition 1.2.17 and the preceding...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of the proof of Proposition 1.2.17 ... ... Duistermaat and Kolk's Proposition 1.2.17 and the preceding...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of the proof of Lemma 1.8.2 ... ... Duistermaat and Kolk"s Lemma 1.8.2 and the preceding definition and notes...

Homework Statement Consider the circuit How long after the switch is closed does the voltage across the resistor drop to Vf = 20V. Answer in units of s. Homework Equations Tc = RC Q=Qm(1-e-t/RC) The Attempt at a Solution [/B] RC = .0003026 11 = 31(1-e-t/RC) .3548 = 1-e-t/RC 1.3548 =...

Hey. I really like the topic of Closed Timelike Curve's, they're an interesting subject matter, since they're allowed by certain field equations of GR. I was curious if there is any way (in the future?) we could warp spacetime to create a CTC, and maybe harness it? Could be useful.. ish. Thanks.

Homework Statement Hello Everyone, a pleasant good morning to all :) I will attach an image that shows a diagram of a circuit. The question based on this picture is as follows: ''When switch S is closed, the Lamp L, lights. Explain how this occurs.'' Homework EquationsThe Attempt at a Solution...

I am reading "Multidimensional Real Analysis I: Differentiation by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of the proof of Lemma 1.2.10 ... Duistermaat and Kolk"s proof of Lemma 1.2.10 (including D&K's definition of a...

Homework Statement Find (a) the module and (b) the direction, entering or exiting the page plane, of the magnetic field at point P, knowing that a = 4.7 cm and i = 13 A Homework Equations Biot-Savart law The Attempt at a Solution For 1-2 and 4-5 segments, B = 0 because sin θ = 0 for...

Homework Statement The question is Derive an expression for the closed loop gain of the differential amplifier. I have solutions for these questions but the solution for this question is quite vague. Here is the solution: I understand part 1 and part 3, but part 2 I don't. So looking at...

[Moderator's note: split off from another thread since this is a separate topic.] I am confused about closed timelike curves. To say that they are possible using an exact solution to the EFEs, like the Godel metric, and that they actually correspond to something in reality is where my confusion...

[Moderator's Note: Thread title changed to better reflect the problem statement] Homework Statement A body of mass m is on a disk of mass M=2m and radius R, initially static and free to spin around its center. The mass mm goes around a trajectory described in the image below with constant...

In a closed fluidic system (with a pump), fluid velocity is constant throughout the system but what puzzles me is the pressure drop due to viscous effect. In a horizontal pipe, pressure decreases gradually (assuming low friction) down the pipe due to viscous effect. In this concepts, it's hard...

What causes there to be a node at a closed end of an air column and an antinode at the open end of a air column? Why doesn't it change as the wave oscillates?

So let's say I do the reaction Mg + HCl --> MgCl2 + H2 in an open calorimeter. I measure a certain temperature change in the calorimeter, let's say an increase of 12 degrees C. Keeping all other variables the same, if I perform this experiment in a closed calorimeter, what will happen to the...

I was out and about today and observed a dog walker playing frisbee with their dog. I noticed the frisbee gliding gracefully through the air as the dog jumped to grab it, clutching the ring-like disc in its mouth. It got me to thinking about airflow over the disc, the lift and drag properties...

Let $S_n(k)$ be defined by: $S_n(k) = 1 + 2k+3k^2+...+(n+1)k^n$, where $|k| < 1$ and $n \in \Bbb{N}$. Derive a closed form for $S_n(k)$ and find the limit: $$\lim_{{n}\to{\infty}}S_n(k)$$.

I'm reading this proof on the matter: https://math.stackexchange.com/questions/278755/show-that-a-retract-of-a-hausdorff-space-is-closed How do we know that the final neighborhood they come up with is disjoint from A?

Homework Statement Suppose that pn → p and each pn lies in lim S. We claim that p ∈ lim S. Since pn is a limit of S there is a sequence (pn,k)k∈N in S that converges to pn as k →∞. Thus there exists qn = pn,k(n)∈ S such that d(pn, qn) <1/n. Then, as n→∞ we have d(p, qn) ≤ d(p, pn) + d(pn, qn) →...

Homework Statement Suppose that S is a closed set. We claim that Sc is open. Take any p ∈ Sc. If there fails to exist an r > 0 such that d(p, q) < r ⇒ q ∈ Sc then for each r = 1/n with n = 1, 2, . . . there exists a point pn ∈ S such that d(p, pn) < 1/n. This sequence in S converges to p ∈ Sc...

Homework Statement Let ##E## be a closed set of real numbers and ##f## a real-valued function that is defined and continuous on ##E##. Show that there exists a function ##g## defined and continuous on all of ##\Bbb{R}## such that ##f(x) = g(x)## for each ##x \in E##. Homework EquationsThe...

Hello! I have a problem : I have an elastic container (I call it "balloon"). I fill it 100% with water (no air bubbles) and close it. There is a pressure sensor connected to the balloon to measure the pressure inside it. I would like to ask You : what factors have influence on the pressure...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (3) ... ... Exercise 2.2.4 Part (3) reads as follows: I am unable to make a meaningful...

Homework Statement I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (3) ... ... Exercise 2.2.4 Part (3) reads as follows: Homework...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with a part of Exercise 2.2.4 Part (2) ... ... Exercise 2.2.4 Part (2) reads as...

Hello! Hopefully someone here can help with this problem: I have a condenser that holds 35 gallons of water to cool the copper coil on my still. I need to know if I can create a closed loop system of cooling water that allows me to avoid running a chiller. I know that there is probably an...

I'm not a math machine, but I dabble in dimensional stuff. I think this falls under knot theory. I have built several prototypes of a tesseract. Each of them sits in a little case in my office. One of them is made from truncated cubes, held together with elastic cord: In theory, the...

Hi all, I have a question about the effect of partially closing a pump discharge valve on the system curve, wondering if you guys can help me out. Right now I have the yellow pump curve and the orange 2 inch system curve , producing around 120 gpm against around 110 ft of head. If I expand...

I googled a lot on proof of Gauss theorem and nearly every other proof (on web and so on books) state that solid angle of closed surface is 4pi but I can't find the proof of this nowhere ! I tried setting up the integral but don't know how to proceed furthur : Ω=∫(cosθ/r^2)*dA Also The one...

I was trying to show that a closed interval ##[a,b]## and ##\mathbb{R}## cannot be homeomorphic. I would like to know whether this can actually be considered as a proof. It is the following: - The closed interval ##[a,b]## can be written as ##[a,p] \cup [p,b]##, where ##a \leq p \leq...

Hi everybody, I'm a PhD student working on solution-processed kesterite PV cells. The material is spin-coated and I personally believe that its wetting properties are influenced by environmental parameters like temperature and humidity. To control these parameters, or at least reduce their...

I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location. Suppose there is an observer S on a planet and an observer S'...