# Topology and Analysis

- Point-set topology. Real, complex, harmonic and functional analysis. Measure and integration theory
 Meta Thread / Thread Starter Last Post Replies Views Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 10:25 AM micromass 1 23,602 I've learned some complex analysis from the book written by James Brown and Ruel Churchill, but I forget almost... Dec4-13 08:46 PM Jorriss 1 237 Moved: Infinite series. - - - Moved: Infinite series. - - - I'm having some trouble understanding why cuts are defined with property 3 below: "A cut in Q is a pair of subsets... Dec2-13 09:00 PM R136a1 1 127 How can I find all analytic functions f=u+iv with u(x,y)=(x^2)+(y^2) Thanks for the help. I appreciate it. Dec1-13 10:07 AM HallsofIvy 5 287 My first analysis/topology text defined the boundary of a set S as the set of all points whose neighborhoods had some... Dec1-13 02:01 AM economicsnerd 1 93 Hi, We have: \beta(a,b)=\int_0^1 t^{a-1}(1-t)^{b-1}dt,\quad Re(a)>0, Re(b)>0 and according to Wikipedia: ... Nov30-13 02:25 AM jackmell 11 861 Hi guys, just wanting to know if I'm doing this right. f(z) = \frac{z}{(z^2 + 4) (z^2+1/4)} Singularities of f(z)... Nov29-13 11:54 AM Office_Shredder 3 119 Given this definition of two homeomorphic spaces, Deﬁnition 1.7.2. Two topological spaces X and Y are said to be... Nov27-13 11:50 PM Streltsy 9 369 One of the definitions of a subbasis ##\mathcal{S}## of a set ##X## is that it covers ##X##. Then the collection of... Nov25-13 02:33 PM economicsnerd 4 252 How can one show that a positive function with a Lebesgue integral is measurable with respect to the complete sigma... Nov23-13 10:40 AM AlexChandler 4 477 What do all possible combinations of the pochhammer contour over the normal Riemann surface for the function... Nov23-13 08:16 AM jackmell 0 159 May I ask what is the ramified branching geometry of the algebraic function: $$w=z^{p/q}(1-z)^{r/s},\quad... Nov23-13 06:19 AM jackmell 1 222 Quick question about the metric space axioms, is the requirement that the distance function be positive-semidefinite... Nov21-13 11:48 AM gufiguer 19 675 I could use some insight in the form of a summary. Can the topology of a manifold determine the metric use on it?... Nov20-13 11:29 PM gufiguer 11 607 The topology ## T ## on a set ## X ## generated by a basis ## B ## is defined as: T=\{U\subset X:\forall\ x\in U\... Nov20-13 11:02 PM gufiguer 18 428 I am currently reading Munkres' book on topology, in it he defines an open sets as follows: "If X is a topological... Nov20-13 07:24 PM 1MileCrash 5 293 I was recommended Rudin's "Principles of Mathematical Analysis" as a text that assumes you know nothing and takes it... Nov20-13 06:22 PM gufiguer 30 1,264 I've just started working through Rudin's Principles of Mathematical analysis. In my opinion, the choice of symbols... Nov20-13 05:02 PM gufiguer 4 464 Here's a claim: Assume that a function f:\to\mathbb{R} is differentiable at all points in its domain. Then the... Nov19-13 05:17 PM jostpuur 11 452 Given the algebraic function:$$w=z^{p/q}(1-z)^{r/s},\quad (p,q,r,s)\in\mathbb{Z}\backslash\{0\}$$and I choose... Nov19-13 06:49 AM jackmell 0 262 So far, I have encountered the following formulations of completeness and was wondering whether they are all... Nov17-13 10:52 PM Bipolarity 0 212 Let f(x+iy) = \frac{x-1-iy}{(x-1)^2+y^2} first of all it asks me to show that f satisfies the Cauchy-Riemann... Nov17-13 09:18 PM economicsnerd 3 300 hello everybody I'd like to understand what mean the result of a complex integral. For example, integrate f(z) = z²... Nov16-13 05:56 PM Erland 6 416 If I have a x,y table of discrete datapoints with a discrete dataset, such that delta x is not a constant, what are... Nov15-13 10:18 PM AlephZero 2 356 I am reading H. Croom's Principles of Topology and in page 139, he gave an example 5.2.5 to show that two points in... Nov15-13 04:40 PM qinglong.1397 2 291 If there is a formula relating the exponential with sine and cosine normal and hyperbolic (exp(ix) = cos(x) + i... Nov14-13 06:18 PM lurflurf 9 284 In the textbook I am working with, an isolated point of A is defined to be a point X in A such that there exists a... Nov11-13 04:57 AM Axiomer 3 338 In Theorem 1.21, Rudin says: The identity b^n-a^n=(b-a)(b^{n-1}+b^{n-2}a+....+a^{n-1}) yields etc etc. What is... Nov9-13 09:51 AM bhagwad 6 437 I'm struggling with the concept of uniform continuity. I understand the definition of uniform continuity and the... Nov8-13 05:00 PM Erland 18 831 Let f:N-> Q be a bijection. I want to show that this is uniformly continuous on N. (N is the set of natural numbers, Q... Nov7-13 01:09 PM deekin 1 297 The Maclaurin series expansion for ##(1+z)^\alpha## is as follows:$$(1+z)^\alpha = 1 + \sum_{n=0}^\infty... Nov2-13 04:17 PM mathman 1 309 Is there any relation between compact embedding and dense embedding? Thanks in advance for your reply. Nov1-13 10:35 AM Tatianaoo 4 305 The windowed Fourier transform on R Defi nition-Proposition-Theorems (Plancherel formula-Parseval... Nov1-13 08:49 AM m.a.math 0 281 Given: f\left(\frac{az + b}{cz + d}\right) = (cz + d)^kf(z) We can apply: \left( \begin{array}{cc} a & b \\... Oct30-13 06:47 PM Parmenides 0 308 hello friends, when i build the mathmatical model of robot,i face a new question that i ever seen before. i have a... Oct30-13 04:22 AM jonasjia 4 522 According to Fractional Calculus, the power rule can be written as (dm/dzm) zn = n!/(n-m)! zn-m For example, ... Oct27-13 05:26 AM Harrisonized 0 325 Everything here is in a Hilbert space. If x_n\to x and y_n\to y in norm, then under what conditions does \to... Oct27-13 02:10 AM pwsnafu 11 560 if A is a subset of B and the frontier of B is a subset of A then A=B. I am pretty sure that this is true as I drew... Oct26-13 10:49 AM HallsofIvy 4 373 Consider the classical wave equation in one dimension: \frac{\partial^2 \psi}{\partial x^2}=\frac{1}{v^2}... Oct26-13 07:10 AM epr1990 3 540