Closed Definition and 1000 Threads

"Open" and "closed" relations We know that if we have convergent sequences (xn) and (yn) in simply ordered metric space, then xn\leqyn implies that the limits x and y have x\leqy. Also, xn<yn. My instinct on noting this is to say that "<" is an "open relation" on that metric space, and that...

Would it be possible to observe our own Milky Way Galaxy developing in its early stages? Or at least possible for a very old galaxy to observe itself developing in it's infant stages?

Hi guys! I am reading a paper which uses closed forms \omega on a p-dimensional closed submanifold \Sigma of a larger manifold M. When we integrate \omega we get a number Q(\Sigma) =\int _{\Sigma}\omega which, in principle, depends on the choice of \Sigma but because \omega is closed...

Hello, Please forgive my ignorance, although bright, I was a lousy student, & never took physics in school. I find it frustrating when relatives & friends are uncertain as to how to respond to questions like those below, so your educated reply would therefore be all the more appreciated...

Hi, Is there a characterization of subsets of the Cantor space C that are closed but not open? As a totally-disconnected set/space, C has a basis of clopen sets; but I'm just curious of what the closed non-open sets are.

Homework Statement Suppose V is a vector space. Is the set of all 2x2 invertible matrices closed under addition? If so, please prove it. If not, please provide a counter-example. Homework Equations The Attempt at a Solution well i know that what does it mean to be closed...

Hello, i just came accros: Sum(i) , from i=1 to i=n which apparently equals n(n+1)/2 -Is there a way to derive this from the sum, or you just have to use your intuition and think through what exactly is being summed and the range of summation? -Do you have any resources to offer, that...

Let us consider the cosmological metric: {ds}^{2}{=}{dt}^{2}{-}{[}{a}{(}{t}{)}{]}^{2}{[}\frac{{dr}^{2}}{{1}{-}{k}{r}^{2}}{+}{r}^{2}{(}{d}{\theta}^{2}{+}{sin}^{2}{(}{\theta}{)}{d}{\phi}^{2}{]} -------------- (1) For closed models k is positive We shall consider here a closed one: We write...

Anyone have a good example of a closed subset of a topological space that isn't closed under limits of sequences?

A simple rotating system with no external forces acting on it carries a fixed angular momentum and an associated rotational kinetic energy. If the system changes its internal configuration, such as a spinning skater retracting or extending his/her arms, the angular momentum remains constant...

From the definition of an open set as a set containing at least one neighborhood of each of its points, and a closed set being a set containing all its limit points, how can we show that the complement of an open set is a closed set (and vice versa)? Usually this is taken as a definition, but...

Homework Statement prove that the set of continuous functions on [0,1] that are increasing is a closed set. Homework Equations The Attempt at a Solution Need to prove the complement is open. So need to prove the set of continuous functions on [0,1] that are non increasing is open...

The 405 fwy in Los Angeles will be closed for construction work. For anyone who has to drive in the area, what a nightmare this will be! Last night on the Tonight Show, Jay Leno actually played a video of alternate routes...

suppose i have a bucket full of water in a closed room,the water is kept undisturbed for say 5 days,after those 5 days i found that the temperature of water was lower than as it was 5 days before and so it does for the room all this (for the system) isn't going in accordance with second law of...

im on the topic of electricity and magnetism, and came across walter lewin's lecture. i cannot visualise how the 'open surface' of this solenoid will look like is the open surface a riemann surface? or something else...

Hello, I am trying to think of examples of these. At the moment, I can only think of ( on R ) closed intervals being the union of single-point sets ( infinitely many, the ones inside ).. et c. I also think the cantor set is an example of this. Are there more "natural" examples? Thank you for...

do they exist in reality or in nature?

a closed set contains all its cluster (accumulation) points: points for which any open neighborhood around them no matter how small contains points from the set. a complete set contains all limit points of Cauchy sequences. which are very similar to cluster points. My question is: in a metric...

Homework Statement Dn={f in C([0,1]) : there exists t in [0,1] for every h in R/{0}, abs((f(t+h)-f(t))/h) <=n} prove the Dn's are closed nowhere dense sets. A subset of some set A is closed in A if its complement is open in A. Homework Equations The Attempt at a Solution i...

Hi, All: Let X be a metric space and let A be a compact subset of X, B a closed subset of X. I am trying to show this implies that d(A,B)=0. Please critique my proof: First, we define d(A,B) as inf{d(a,b): a in A, b in B}. We then show that compactness of A forces the existence of a in A...

So basically, my metric space X is the set of all bounded functions from [0,1] to the reals and the metric is defined as follows: d(f,g)=sup|f(x)-g(x)| where x belongs to [0,1]. I want to prove that the set of all discontinuous bounded functions, D[0,1] in X is open. My attempt - Start with an...

Homework Statement I have been self studying Spivak's Calculus on Manifolds, and in chapter 1, section 2 (Subsets of Euclidean Space) there's a problem in which you have to find the interior, exterior and boundary points of the set U=\{x\in R^n : |x|\leq 1\}. While it is evident that...

Hi everyone. I am currently carrying out an experiment whereby I have a closed tank of water submerged in a larger tank. The water in the smaller box is heated and I am interested in the heat loss from the tank. I have done a rough theoretical calculation based on U values, where by I obtain...

Homework Statement A closed surface with dimensions a = b = 0.294 m and c = 0.3528 m is located as in the figure. The electric field throughout the region is nonuniform and given by \vec{}E = (\alpha+\beta x2)ˆı where x is in meters, \alpha = 2 N/C, and \beta = 4 N/(Cm2). See figure...

Hi. I'm trying to find a good definition of a closed linear subspace (as opposed to any other linear subspace), and I can't find anything concise and comprehensible. Any help will be much appreciated. P.S. I'm not great at analysis, so please try to keep it simple.

I did an experiment in class to determine the speed of sound. I used the speed of sound in air equation with the room temp at 28°C which was calculated at 348.6m/s. However when doing the experiment I got 329m/s. I just want to know some source of error that may have caused this? I have...

Let X be any infinite set. The countable closed topology is defined to be the topology having as its closed sets X and all countable subsets of X. Prove that this is indeed a topology on X. Any help would be greatly appreciated. Thanks!

Hi. I am trying to find the classical turning points in semi-parabolic coordinates for the hydrogen atom when an electric field is being applied to it in the y-axis. I am reading an article for those who are interested called Classical, semiclassical, and quantum dynamics in the lithium Stark...

Greetings, for the school I must find some information about the building of a small close wind tunnel . Some one know where to find it? Good day!

There the well known theorem that every open set (I'm talking about R here with standard topology) is the union of disjoint open intervals. Now, looking at the geometry, it seems that between any two adjacent open intervals which are in the union constituting our open set there is a closed...

Homework Statement I tried using \ooiint, I want a loop that circles both integrals (two), anyone know?

Q) A closed chamber containing working refrigerator is pefectly insulated and d door of refrigerator is opened, wat ll happen to temperature inside the chamber a)Decrease b) Remain same c) Increased d) Cant say coz it depends on quality of insulation

Homework Statement show that (the range of) a sequence of points in a metric space is in general not a closed set. Show that it may be a closed set. 2. The attempt at a solution I don't know where to start. For example, if we are given a sequence of real numbers and the distance...

f(x)=1/x closed set?? A book I'm reading now says the graph of f(x)=1/x is a closed set, how come?? Its range is [(-\infty,0)\cup (0, \infty). A set is closed iff every convergent sequence has a limit point in the set. If a sequence converges to 0, then 0 is not in the range

Hi, i want to understand how fundamental group of a closed oriented 3-mfd determines all its homology and cohomology gorups. Please can you help me.

Assume X is a metric space, then X and the empty set are both closed and open, am I correct?

In a closed piping system (such as a chilled or hot water system in a tall building), is the water pressure at the top less than that at the bottom? Bernoulli's equation would lead you to believe that it is, but I cannot find anything explicitly stating that this applies to closed systems...

Homework Statement 1. Find an uncountable number of subsets of metric spaces \left(\mathbb{R}^{n},d_{p}\right) and \left(\mathbb{C}^{n},d_{p}\right) that are neither open nor closed. 2. If 1\leq p<q , then the unit ball in \left(\mathbb{R}^{n},d_{p}\right) is contained in the unit ball in...

Hi, one of the problems that inflation right after the Big Bang solves is the horizon problem. While this post is not really related to inflation, I was wondering why a closed universe is not a more favorable candidate for the solution to that problem, rather than inflation. Perhaps I...

Homework Statement Given \mathbf{F} = \nabla f\; where \;f(x,y) = sin(x-2y) Find a curve C that is not closed and satisfy the equation \int_C \mathbf{F}\cdot dr = 0The Attempt at a Solution \nabla f = \;<cos(x - 2y),-2cos(x-2y)> So to satisfy the dot product being 0 (I am hoping I can do...

Ok this is solely for my interest. I should know this if I were taking Grade 12 Chemistry, but I haven't had this course in two years, and neither have I continued in pure science since then so please if you know better tell me if this is correct AND if it is only so because the case is of a...

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Homework Statement If Dr is a closed disk of radius r centered at (a,b) find lim r->0 (1/pir2) \int\intfdA over Dr. The Attempt at a Solution From mean value equality, \int\int fdA = f(x,y)A(D) where A(D) is the area of the region which here is pir2. So the lhs becomes lim r->0 f(x,y)...

Hello everyone, curious about something here. I saw a demonstration lately were a magnet was dropped down a copper pipe and the magnet dropped very much slower than expected. What I got to thinking was, if you replaced the copper pipe with the same quantity of insulated copper wire in a...

Hi Guys, What does the term Closed form solution mean?

Homework Statement evaluate integral around a closed contour (C) of f(z) dz, where C is the unit circle centred at the origin and f(z) is (sin z)/z Homework Equations The Attempt at a Solution well, the textbooks don't give a similar example

A Union of a FINITE collection of closed sets is closed. But if it is an infinite collection? Can someone provide an example please?

Hello, If I put a voltmeter over a (pn-junction) diode, do I measure anything? I would intuitively say "no". Is the following picture correct? So let's say the P-region is to the right, N-region to the left. If I were to attach a voltmeter across it, I'd have to attach a metal wire...

UC Davis department admissions closed?!? (Anger enclosed) So UC Davis dropped a damn bombshell on me this morning. I applied to the universities Department of Applied Science Graduate Program for the Fall 2011 semester. I get an e-mail this morning, MARCH 31ST, that I'm not even rejected, BUT...

Homework Statement 1kg of water that is initially at 90 degrees celsius with a quality of 10% occupies a spring loaded piston cylinder device. The device is now heated until the pressure rises to 800kPa and the temperature is 250 degrees c Determine the total work done during this process...