Interior Definition and 144 Threads

The question says: Show that if Q = [a1,b1]x...x[an,bn] is a rectangle, the Q equals the closure of Int Q. The definition of closure that I have is Cl(A) = int(A) U bd(A). So I'd like to show that Cl(int(Q)) = int(int(Q)) U bd(int(Q)). But this just seems to be obvious to me which just makes...

Homework Statement I need to prove that the int(U union Bdy(U))=Int(U) when U is open. Homework Equations Bdy(U)=closure(U) intersect closure(X-U) a point is in the interior if there is an open neighborhood of the point that is contained in the set. The Attempt at a Solution...

what is the hell is Interior draeminity?? Hi, this is very strange and i have never heard about it, i either can't find any results in google search.. so what is Interior draeminity?? i have been asked this question in Geosciences workshop in my college kinda of 'testing you knowledge' '...

I'm not sure about my answers, any help is highly appreciated. Let (N, U) be a topological space, where N is the set of natural numbers (without 0), and U = {0} U {Oi, i is from N}, where Oi = {i, i+1, i+2, ...} and {0} is the empty set. One has to find the interior (Int) and closure (Cl) of...

Hello! Homework Statement Find the interior of each set. a.) {1/n : n\inN} b.) [0,3]\cup(3,5) c.) {r\inQ:0<r<\sqrt{2}} d.) [0,2]\cap[2,4] I understand that b.)'s interior points are (0,5). I don't understand why the rest have int = empty set. By definition, if there...

Hello, I have heard the following from several places: The amount of information that can be stored within a sphere is equal to the amount of information that can be stored on its surface. This seems like a contradiction or, a self-defeating statement. It seems to instead say that a...

Homework Statement Let (X,d) be a metric space and let A \subseteq X. Denote the interior of A by A^o. Homework Equations Prove that if A is open or closed, then (\partial A)^o = \varnothing. (Is this still true if A is not open or closed?) The Attempt at a Solution I don't even...

g_{tt} = \left\{ \begin{array}{rcl} \frac{3}{2} \left( 1 - \frac{2GM(r)}{c^2 R} \right)^{\frac{1}{2}} - \frac{1}{2} \left( 1 - \frac{2 G M(r) r^2}{c^2 R^3} \right)^{\frac{1}{2}} \; \; \text{for} \; \; 0 \leq r \leq R \; \text{(interior)} \\ \left( 1 - \frac{2GM(r)}{c^2 R} \right) \; \...

Homework Statement Let (X,d) be a metric space and E is a subset of X. Prove that (c means complement, E bar means the closure of E) Homework Equations N/A The Attempt at a Solution Let (X,d) be a metric space and B(r,x) is the open ball of radius r about x. Definition: Let F be...

Find a parametrization of the curve x2/3+y2/3=1 and use it to compute the area of the interior. What I did was y=(1-x2/3)3/2 I then integrated this function from 0 to 1 (using maple since it is a crazy integral) and got the answer to be 3/32 \pi. However this is wrong, I probably wasn't...

I have to describe the interior of the subsets of R: Z,Q. I don't understand how to tell if these certain subsets are open or how to tell what the interior is, can someone please explain

Homework Statement Let W\subset S \subset \mathbb{R}^n. Show that the following are equivalent: (i) W is relatively closed in S, (ii) W = \bar{W}\cap S and (iii) (\partial W)\cap S \subset W. Homework Equations The only thing we have to work with is the definitions of open and closed sets...

Homework Statement Find the smallest interior angle of the triangle ABC whose vertices are given. A = (3,1,-2), B = (3,0,-1), C = (5,2,-1) Homework Equations I think the equation arccos( U dot V / (lengthU)(lengthV) The Attempt at a Solution What i did is tried the formula for...

Hallo, My teacher wrote that: "The set has no interior points, and neither does its complement, R\Q" where R refers real numbers and Q is the rationals numbers. why can't i find an iterior point? thanks, Omri

Consider a cone's surface with its vertex subtending a right angle and its base removed. If its interior were silvered, how would an observer on the axis of symmetry appear in its reflection?

Homework Statement A ranger in tower A spots a fire at a direction of 321 degrees. A ranger in tower B, located 60 mi at a direction of 47 degrees from tower A, spots the fire at a direction of 279 degrees. How far from tower A is the fire? How far from tower B? Homework Equations...

I was looking for a space time metric that describes the INTERIOR of spherically symmetric rotating stars. However, wherever I look it is always the metric for an exterior of "slowly rotating star" (frame dragging effect) or something similar to it but always the metric AROUND the object...

Homework Statement If D\subsetR, then x\inD is said to be the interior point of D iff there is a neighborhood Q of x such that Q\subsetD. Define D^{\circ} to be the set of interior points of D. Prove that D^{\circ} is open and that if S is any open set contained in D, then S\subsetD^{\circ}...

Homework Statement Let S be a set in R^n, is it true that every interior point of 'the closure of S' is in Int S? Justify. 2. Relevant theorem S^int = {x belongs to S: B(r,x) belongs to S for some r>0} The closure of S is the union of S and all its bdary points. The Attempt at...

They give me a table of ion concentrations of the most common ions in the cell interior and in the blood. I am asked to calculate the conductivity of the cell interior and that of the blood. I have no idea how to calculate conductivity if I only know the concentrations. Here is the table I am...

Let S be a set in Rn, is it true that every interior point in the closure of S is in the interior of S? Justify. ie. int(closure(S)) a subset of int(S) It seems to me that it would be true...if you could say that the interior of the closure of S is the interior of S unioned with the...

I have come across some window mount unit solar cell that power little exhaust fan that claims to coll down the car cabin that parked under hot summer sun. However since the fan is not powerful enough to drive the heat out of the car effectively, is it enhance it with: 1. larger solar panel...

I have done enough interior/exterior painting to have a general idea of what I am doing, but I have a couple of questions? When you are painting an interior wall and you are 'cutting in' at the ceiling, do you: (a) use the brush vertically and paint from the ceiling downward...

Earth’s interior is much hotter than the surrounding environment (i.e., empty space) so there must be a tendency of the Earth to expand - yet the Earth’s volume remains essential constant. This is so because an equilibrium has been achieved in which the heat-driven expansion is balanced by a...

Homework Statement I want to show that every polygon with more than 3 sides has an interior diagonal. Homework Equations The Attempt at a Solution If the polygon is convex, this is obvious. If not, there is an interior angle at some vertex, say V, that is greater than 180 degrees. Then I think...

A couple years ago on Nat Geo they were showing something about how tornadoes don't actually spin on the inside but they have air that goes up and down because of pressure. The show was saying on the outside they spin but the closer in you go because of the air pressure it sucks and throws...

a. 1/n + 1/m : m and n are both in N b. x in irrational #s : x ≤ root 2 ∪ N c. the straight line L through 2points a and b in R^n. for part c. i got: intA= empty ; bdA=clA=accA=L Is this correct? how about part a and part b...i am so confused...

[SOLVED]Finite-Compliment Topology and intersection of interior Homework Statement Given topological space (R^{1}, finite compliment topology), find counter example to show that Arbitary Intersection of (interior of subset of R^{1}) is not equal to Interior of (arbitary intersection of...

Homework Statement Can a complete metric space have empty interior? Homework Equations In mathematical analysis, a metric space M is said to be complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M. The Attempt at a Solution But if M has no...

For a polygon with n sides, the sum of the interior angles is 180n - 360. If we find n positive numbers that sum up to 180n - 360, does that necessarily mean these numbers can be represented as the inside angles of a polygon with n sides? I can't prove this right or wrong...

does a set with empty interior have measure zero? I think it does...

Last night I watched a program on TV that made the statement that in the interior of our sun the gravity is so intense that a photon of light can travel only several thousandths of an inch per minute. It takes hundreds of thousands of years for a photon of light to travel from the interior of...

SO i have a problem that's "AB ll CD, Find x and y". I got the answer of x=48, =144 Because first the measure they already gave you was 42. As well as y - 12for the other angle measure. And x was the measurement for D. blah it's too hard to explain but i got it correct. My point is that in...

Anybody know where to find a listing of the Spherical Interior Angles for Regular and Archimedean Solids. For example on a Buckyball (Archimedean Solid - truncated dodecahedron) should have angles: A: Angle between vertexes (length of Edges in radians) B: Angle from center Hexagon to...

Hi. Can somebody please check my work!? I'm just not sure about 2 things, and if they are wrong, all my work is wrong. 1. Find a counter example for "If S is closed, then cl (int S) = S I chose S = {2}. I am not sure if S = {2} is an closed set? I think it is becasue S ={2} does not have an...

I am confused with the terms Relative Interior of a set and Interior of a set. Can someone enlighten me. Also, there is a term Relative Boundary. What does this relative signify?

Right I have been given the following problem and cannot resolve it. I have had an attempt but without much success. Could anyone help me with this exercise, please? Hints or a little more welcome :-) A cyclic hexagon is a hexagon whose vertices all lie on the circumference of a circle...

This gigantic thing here called the Centauri Princess, can it be built in the next few hundred years? http://www.astroscience.org/abdul-ahad/firstarktoalphacentauri.htm That would be the greatest engineering achievement in all human history...

Hi everyone, I'm having difficulty with an exercise I have to do in differential geometry this semester. Suppose that the interior product (also known as the interior derivative) is denoted by i_X . Then the exercise is to show that: i_X\star\omega = \omega\wedge X^\flat where...

If A \subset X where X has a topology, is it generally true that the interior of A is equal to the interior of the closure of A? This seems very reasonable to me, but probably only because I'm visualizing A as a disc in the real plane. If it isn't true, what would be a counterexample? thanks

Explain me why the sum of the interior angles of a triangle is not equal to 180 degrees on a spherical surface?

hi, today, my teacher told us that if you draw a triangle on the surface of a sphere, you'll get a triangle with interior angle of not 180 degree, also, if you draw a triangle in a trumpet like shape, you'll get a triangle with 0 degree.. where can i find more infomation about this theory?

hi ppl, How do these guys http://www.solarmissiontechnologies.com/ work out what the interior temperature will be and how fast the resulting hot air will move? thanks :) CJ

If you let go two oposite charges from distance D they will start to attract and if they can pass thru each other when they meet they will distant them selfs until they reach -D distance. They they will start geting back until they get to the initial distance D. This domain from D to -D via the...