Interior Definition and 149 Threads

Interior design is the art and science of enhancing the interior of a building to achieve a healthier and more aesthetically pleasing environment for the people using the space. An interior designer is someone who plans, researches, coordinates, and manages such enhancement projects. Interior design is a multifaceted profession that includes conceptual development, space planning, site inspections, programming, research, communicating with the stakeholders of a project, construction management, and execution of the design.

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  1. P

    Do vacuum vessels have issues with the interior layers flaking off?

    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...
  2. O

    MHB Proving Interior Point of A if x in A: R^p

    i was given that A= B(0,1)={x in R^2| 2-norm of x is less than 1} show that x in R^p is an interior point of A iff x in A my work i managed to prove this one way and struggling with the other, well a bit confused i said assume that x is an interior pt of A then: B(x,r) is a subset of A. but x...
  3. A

    Determine the interior, the boundary and the closure of the set

    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...
  4. G

    Notes on interior lighting circuits (?)

    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...
  5. Markus Hanke

    Is Weyl Curvature Present in Interior Spacetimes?

    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...
  6. J

    What Are the Utilities of Interior and Exterior Products?

    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.
  7. adjacent

    Will a 100% Reflective Interior Box Explode if a Light Source is Placed Inside?

    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...
  8. P

    Interior points proof where one set is a subset of the other

    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?
  9. S

    Can interior pressure of a tornado be calculated?

    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?
  10. F

    Local flatness at r = 0 for star interior spacetime

    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...
  11. P

    What is an effective approach to proving that interior points are open?

    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...
  12. harrylin

    Are Finkelstein/Kruskal Black Hole Solutions Compatible with Einstein's GR?

    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...
  13. D

    Spectrum of singular Sturm-Liouville operators with singular interior point

    Hi, I have a singular Sturm-Liouville problem with LCNO end-points, but also one limit circle point in the interior of the interval. Suppose I take boundary conditions that get me a self-adjoint extension of the differential operator, does anyone know if that gives me a discrete spectrum...
  14. O

    MHB The Supremum of a Set is not an Interior Point

    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\}...
  15. F

    Interior metrics and circular orbits

    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...
  16. T

    Interior and boundary of set of orthogonal vectors

    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...
  17. C

    Does Cl(X-A)=X-Int(A) work in infinite and uncountable dimensions?

    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.
  18. C

    Excluded Point Topology: Int(A) and Cl(A) for Sets A with or without p in X

    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...
  19. M

    Interior of a Set in a Metric Space: Explained

    "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...
  20. H

    Prove: If p has a neighborhood contained in A, then p is in the interior of A.

    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...
  21. H

    Show If a point A is in the interior, then it has a neighborhood contained in A.

    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}...
  22. B

    Exploring the Cantor Set: Why There Are No Interior Points

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

    Topology generated by interior operator

    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...
  24. L

    Is the interior of an angle a convex 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.
  25. B

    Clopen Sets: Closure = Interior?

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

    Interior angles of polygon on a sphere

    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
  27. V

    Why Does My 12V LED Light Strobe When Connected to a 24V Source?

    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...
  28. J

    Interior Product: Find from Exterior Product

    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?
  29. stripes

    Accumulation points must be interior or boundary points.

    Homework Statement Prove the following: an accumulation point of a set S is either an interior point of S or a boundary point of S. Homework Equations None The Attempt at a Solution Suppose x is not an interior point. Then you cannot find a neighborhood around x such that N is a...
  30. W

    Interior of Exterior of a looped domain

    The photo below is a picture of a problem in my complex analysis textbook but a topology question occurred while I was reading it. (Just to avoid any confusion, I have not taken a topology class yet.) The problem is asking to compute the integral (at the top of the picture) around the closed...
  31. K

    Apostol definition of interior point and open set

    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...
  32. B

    Should I Scale My Boundary Condition Values for Problem Where I Scaled Interior?

    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...
  33. G

    Interior points of the closure of A

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

    Are interior points also limit points

    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...
  35. J

    Are limit points and interior points of a set contained in the set?

    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...
  36. S

    Lumped capacitance model if you insure the interior is well mixed?

    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...
  37. C

    Pressure on a Sphere due to an Interior Force

    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?
  38. T

    Topology - Interior of set - Rudin

    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...
  39. DaveC426913

    Where Can I Find a Colour Picker for Masculine Interior Design Palettes?

    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...
  40. F

    Tortoise-like coordinate transform for interior metric

    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...
  41. M

    A set of real numbers whose interior is empty

    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...
  42. TrickyDicky

    Schwartzschild exterior and interior solutions

    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...
  43. J

    Proof of a relationship between interior and closure

    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...
  44. D

    Confused with closure and interior

    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...
  45. I

    Interior temperature of a solar collector

    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...
  46. L

    Interior, Closure, Boundary and Cluster Points of a Set

    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...
  47. J

    Interior angles of a regular polygon

    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...
  48. Rasalhague

    Interior Product: Definition, Inner Product & Isomorphism

    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...
  49. S

    Finding the set of interior points, the closure, and an example

    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...
  50. K

    If A is contained in B, then the interior of A is contained in B.

    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...
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