Interior Definition and 144 Threads

I've heard of issues in low pressure chemical reactors where the interior scaling might flake off when a vacuum is pulled. Which principles govern this? I know it has to do with internal shear forces and am wondering if a vessel wall would ever split in half. I saw this related...

Homework Statement Determine the interior, the boundary and the closure of the set {z ε: Re(z2>1} Is the interior of the set path-connected? Homework Equations Re(z)=(z+z*)/2 The Attempt at a Solution Alright so z2=(x+iy)(x+iy)=x2+2ixy-y2 so Re(x2+2ixy-y2)= x2-y2 >1 So would...

So basically I'm in the 1st year of EE and we're going to design the wiring diagram. Pretty much all we put at this stage are grounded electricity sockets, lights, water heater, and the oven. The problem is that the book that I've gotten from my school is 95% about mechanical drawings, which...

I am just wondering - is space-time curvature in the presence of energy-momentum ( i.e. in interior solutions to the EFEs ) always pure Ricci in nature ? I had a discussion recently with someone who claimed that, but personally I would suspect that not to be the case in general, since I see no...

I'd like to know what does and which the utility of the Interior (http://en.wikipedia.org/wiki/Bivector#The_interior_product) and Exterior (http://en.wikipedia.org/wiki/Bivector#The_exterior_product) Products.

A light source(powered with a battery) is put inside a box of interior covered with 100% reflective material.(atleast very much reflective).So,photons emitted from the light will not be absorbed.What will happen to the box?Will it's mass increase or will it just blow?What may be the possible...

How would I go about proving that if A is a subset of B then the interior points of A are a subset of the interior points of B?

Can the interior pressure of a tornado be calculated from the centrifugal speed of the tornado and its radius (centripetal force)? For example, given a tornado with a 1/2 mile radius and a centrifugal speed of 200 mph, how much would the interior air pressure be?

Hi All, I am interested in the discussion in section 10.5 of Schutz's First Course in GR book. Specifically, the conditions at r = 0 of a static, spherically symmetric interior star (or whatever) solution e.g. Schwarzschild interior solution. He argues that by enforcing local flatness one...

Homework Statement For S \subset Rn, prove that S° is open. Homework Equations S° are all interior points of S. The Attempt at a Solution My class has only learned how to use balls to solve these types of problems (no metric spaces). So I need to choose an ε > 0 so that Bε(x) \subset...

Are Finkelstein/Kruskal interior black hole solutions compatible with Einstein's GR? This topic is a spin-off from a number of recent discussions: "Are "flowing space" models compatible with GR?" "Schwartzchild and Synge once again" "Oppenheimer-Snyder model of star collapse" "Notions of...

Hello everyone! Given a set A that has a supremum $\alpha$, I want to show that $\alpha \notin int(A)$. Is the following proof accepted? $\alpha = \sup A$ so $\alpha$ is a limit point of $A$. If $\alpha \notin A$, we are done. Otherwise, for $\forall r>0$, we have $N(\alpha,r)-\{\alpha\}...

Hello, I have a couple of questions regarding the calculation of circular orbits in the Schwarzschild exterior spacetime and then the extension of these arguments to other (interior) metrics. First of all, in a few different books/sets of notes there seems to be a bit of 'drift' in the...

Let "a" be a non zero vector in R^n and define S = { x in R^n s.t. "a" · "x" = 0}. Determine S^int , bkundary of S, and closure of S. Prove your answer is correct Attempt: Ok I am more sk having trouble proving that the respective points belong to its condition. Such as thr...

If I have the statement Cl(X-A)=X-Int(A) X and A are topological spaces. Does this statement work in infinite dimensions and uncountable dimensions. I think it would just wondering.

Homework Statement Consider the excluded point topology on a set X. Determine Int(A) and Cl(A) for sets A containing p and for sets A not containing p. Excluded point topology is all the subsets of X that exclude p. where p is in X. The Attempt at a Solution So the interior of...

"In a metric space M with A as a subset, an interior is the largest open subset contained in A." That's how I've written this down in my notes along with some more symbolic definition. If the set within M (say, A) is open would/could the interior also be the whole set? Thanks. Just...

Homework Statement If p has a neighborhood contained in A, then p is in the interior of A.Homework Equations Int A = \bigcup{C\subseteqX:C\subseteqA and C is open in X} By the books definition, a neighborhood is open. The Attempt at a Solution Let C'\subseteqA be a neighborhood of p contained...

Homework Statement Let A be a topological space and let A\subseteqX be any subset. Show: If a point A is in the interior, then it has a neighborhood contained in A. Homework Equations Neighborhoods are defined to be open in my book. Int(A) = \bigcup{C\subseteqA and C is open in X}...

Why there is no interior points in a Cantor set? Please explain me in detail.

Given an interior operator on the power set of a set X, i.e. a map \phi such that, for all subsets A,B of X, (IO 1)\enspace \phi X = X; (IO 2)\enspace \phi A \subseteq A; (IO 3)\enspace \phi^2A = \phi A; (IO 4)\enspace \phi(A \cap B) = \phi A \cap \phi B, I'm trying to show that the set...

I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the intersection of two half planes and using the fact that each half plane is convex. I am stuck on where to go from here.

For a subset which is both closed and open (clopen) does its closure equal its interior?

Hi can anyone help me out with finding the interior angles of a pentagon on a sphere. I know two of the interior angles already and I know all the angles that correspond with the arc lengths of the sides of the pentagon. How do I find the other three interior angles? Thanks

I have a ceiling fan that has a 24v output. It came with a led circuit board to light, however the light is very dim. I purchased a 12v led circuit board to increase the lighting. Now I know that the light is 24v and the new led board is 12v but it was a direct plug in so I thought I would try...

If the interior product is defined as the inverse of the exterior product, then how would I find the interior product of a space given its exterior product?

S is a set such that S\subseteqRn point a is in S: a\inS The point "a" is an interior point of S if there is an open n-ball with center "a", all of whose points belong to S. ie., every interior point of S can be surrounded by an n-ball such that B(a)\subseteqS, where B(a) is the set of...

Hello all: I would very much appreciate advice on setting up a problem. Apologies in advance... This is probably a silly question--I'm more of a chemist than an engineer/math person! I have written a code for calculating changes in concentration/mass within a domain over time, as new...

Is it true? " Set of interior points of the closure of A equals the set of interior points of A. "

Homework Statement Are interior points included in (or part of) limit points? Homework Equations Since the definition of interior points says that you can find a ball completely contained in the set. For limit points, it's less strict, you just have to find a point other than the center.The...

Homework Statement Just wondering if I'm understanding the definitions correctly. I honestly feel like an idiot for asking this. Homework Equations A point p is an interior point of E is there is a neighborhood N of p such that N contained in E. A point p is a limit point if the set...

Hi everybody. I have been doing some experimental heat loss calculations on a sealed cube of fluid, filling the volume of the cube with hot water then sitting it in a larger tank of fluid at a fixed cooler temperature and monitoring the drop of temperature inside the box. I have also positioned...

Consider a sphere of mass M and radius R. The interior of the sphere is a uniformly distributed mass M. The surface shell of the sphere has a certain mass dm. What is the pressure on the surface of the sphere due to gravitational forces?

Homework Statement I am trying to solve part d of problem 9 in chapter 2 of Rudin's Principles of Mathematical Analysis. The problem is: Let E* denote the set of all interior points of a set E (in a metric space X). Prove the complement of E* is the closure of the complement of E. I will...

OK, I've looked for about two hours now and can't find what I want (though I've found lots of stuff that doesn't do what I want.) Years ago, Para Paints had a widget on their site that would have you choose one of about 32 colours, and would then give you a palette that matched it. There's...

Hello! When using the Schwarzschild exterior metric in the klein-gordon equation one can perform the standard tortoise(E-F) coordinate transform to yield a wave equation which has a well defined potential that is independent of the energy term. My understanding is that the motivation for this...

Homework Statement Give an example of a set of real numbers whose interior is empty but whose closure is all of the real numbers if it exists. Otherwise, explain why such example cannot be true. 2. The attempt at a solution For a set S ⊆ X, the closure of S is the intersection of all closed...

Are the interior and exterior solutions described on a common manifold? I mention it because the exterior one is an asymptotically flat space while the interior solution is conformally flat. I'm not sure if a single physical scenario (the vacuum soulution) can be described by two different...

A^closure = X\(X\A)^interior I am REALLY bad at proofs. I never know where to start. I only have the definitions of closure and interior. I feel like they threw us in the deep end I've written like 3pages, but mostly just pictures. interior: a is an element of A^int iff there exists r>0...

Greetings all, I'm looking at some examples in the Topology: Pure and Applied text. Looking at example 2.1 Consider A=[0,1) as a subset of R with the standard topology. Then Aint=(0,1) and Aclos=[0,1]. Can someone explain to me why the union of all open sets in A is that...

Homework Statement A solar collector has an effective collecting area of 12 m^2. The collector is thermally insulated, and so conduction is negligible in comparison with radiation. On a cold but sunny winter's day the temperature outside is -20.0 C, and the Sun irradiates the collector with...

Homework Statement Find the closure, interior, boundary and limit points of the set [0,1) Homework Equations The Attempt at a Solution I think that the closure is [0,1]. I believe the interior is (0,1) and the boundary are the points 0 and 1. I think the limit point may also be...

The number of sides of two regular polygons are in the ratio 5:4 and the difference between their interior angles is 6 degrees.Find the number of sides of the two polygons. I forgot the relation between interior angles and the number of sides of a regular polygon.Can anyone help me to figure...

I think I understand most of this Wikipedia page on the interior product ("not to be confused with inner product"): http://en.wikipedia.org/wiki/Interior_product I can't yet follow the drift of the Wolfram Mathworld page on the same subject...

Suppose that S=[0,1)U(1,2) a) What is the set of interior points of S? I thought it was (0,2) b) Given that U is the set of interior points of S, evaluate U closure. I thought that U closure=[0,2] c) Give an example of a set S of real numbers such that if U is the set of...

Homework Statement Given that A and B are in a topology, show that if A is contained in B, then the interior of A is contained in B. Homework Equations The interior of A:={a: there exists a neighborhood which is a subset of A} The Attempt at a Solution I can prove that the interior of A is...

Homework Statement Prove that if A is a subset of B then int(A) is a subset of int(B). int(A) = interior of A int(B) = interior of B The Attempt at a Solution Take some y E int(a) , this implies that B(r,y) is a subset of A. Given that A is a subset of B, we know that B(r,y) is a subset...

Homework Statement Find all the limit points and interior points of following sets in R2 A={(x,y): 0<=x<=1, 0<=y<=1} *here I used "<=" symbol to name as "less then or equal". B={1-1/n: n=1,2,3,...} Homework Equations The Attempt at a Solution the limit point of B is 1 as n goes to...

Homework Statement S = Set of rational numbers Boundary(interior(S)) = ? The Attempt at a Solution I have no Idea how to do this, I don't know what interior of the rational numbers are. Maybe you guys could give an example of like the interior of the natural numbers or the boundary of the...

Homework Statement Here is a picture of the problem: http://img84.imageshack.us/img84/1845/screenshot20100927at111.png If the link does not work, the problem basically asks: Let "a" be a non-zero vector in R^n. Let S be the set of all orthogonal vectors to "a" in R^n. I.e., a•x = 0 (where •...