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Topology and Analysis

- Point-set topology. Real, complex, harmonic and functional analysis. Measure and integration theory
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:25 AM
1 28,719
What is the relationship with the Mobius strip (or loop) and the 4 dimension? Is Mobius strip a four dimensional...
T 11:28 AM
6 131
I find, in Kolmogorov-Fomin's Элементы теории функций и функционального анализа, at the end of 5 of chapter IV,...
T 10:29 AM
10 175
Edit: I originally wrote that ##\mathcal A## is a Banach algebra. The assumption that goes into the theorem is...
Y 05:46 PM
5 185
I would like to prove , as a subset of R with the standard Euclidean topology, is compact. I do not want to use Heine...
Y 04:31 PM
1 90
Let's say you integrate a complex function along a curve. How do you visualize it? This is explaned very well in...
Sep12-14 09:49 AM
0 95
If I create a bijective map between the open balls of two metric spaces, does that automatically imply that this map...
Sep11-14 05:24 PM
1 103
"In a private project of mine, I have come across a challenging problem. I have 3 points: A, B and C. A is the...
Sep11-14 04:57 PM
2 166
Hi, friends! I find an interesting unproven statement in my functional analysis book saying the image of the closed...
Sep10-14 08:07 PM
2 156
Hello Normally in order to change the order of limit and integration in rimann integration, you need uniform...
Sep10-14 04:27 PM
7 199
The wikipedia article on \sgn (x) ( states that, \frac{d}{dx}\vert...
Sep10-14 09:40 AM
2 157
If I stated a problem that you have to find the solution to the problem x(0) = x_0 < R
Sep10-14 08:49 AM
0 83
hi there, I am trying to prove the following inequality: let z\in \mathbb{D} then \left| \frac{z}{\lambda}...
Sep9-14 03:54 PM
20 433
Dear friends, I read that, if ##A## is a bounded linear operator transforming -I think that such a terminology implies...
Sep9-14 03:25 AM
4 183
integrate e^z/(1-cosz) dz over circle of radius, say 2 i can't seem to recall how it is done. singularity at z=0...
Sep8-14 09:48 PM
8 169
I came across an interesting problem that I have made no progress on. Let f be an analytic function on the disc ##D...
Sep8-14 09:14 PM
5 226
Dear friends, I have been trying in vain for a long time to understand the proof given in Kolmogorov and Fomin's of...
Sep7-14 04:32 PM
10 205
Definition of 'Limit of function (f) at x=p' Let E be domain of f and p be a limit point of E. Let Y be the range...
Sep7-14 06:39 AM
3 150
Before asking a question I would first like to mention the definitions of limit of function and differentiality at x=p...
Sep5-14 06:22 PM
8 217
I just completed a brief introduction to branch points in complex analysis, and I find it difficult to imagine/come up...
Sep3-14 05:44 PM
4 277
How I can show the following \int _{\mathbb{T}} \frac{1}{|1-e^{-i\theta}z|^2}dm(e^{i\theta})= \frac{1}{1-|z|^2}...
Sep3-14 03:47 PM
0 136
Hello, I am facing some problem with Poincare disc. (1) How to visualize a Poincare disc? (2) The arc which...
Sep3-14 12:18 PM
Incnis Mrsi
4 252
Dear friends, my book (an Italian language translation of Kolmogorov-Fomin's Элементы теории функций и функционального...
Sep2-14 07:18 AM
11 237
I read that in any locally convex topological space X, not necessarily a Hausdorff space but with linear operations...
Aug31-14 05:09 PM
4 172
I've taken basic undergraduate Real and Complex Analysis, and I've noticed they focus on different kinds of functions....
Aug30-14 09:39 PM
5 418
I think I've found a proof where Rudin is actually too wordy! For your welcomed inspection, I will type a part of said...
Aug29-14 12:51 AM
4 185
I have to do a project on the dimension theory buy i cant find any info on it. This is the wikipedia page and if you...
Aug26-14 10:00 PM
23 576
How to determine the function from its graph if it has a non-simple shape? Given a graph (see attachment) where set...
Aug24-14 07:32 AM
1 189
I know this post is in the topology thread of this forum, for group theory, this seemed like the reasonable choice to...
Aug23-14 11:21 AM
2 264
Say we have two functions with the following properties: f(x) is negative and monotonically approaches zero as x...
Aug22-14 10:59 AM
2 191
Hi all, Please help! I am reading the paper "A note on contiguity and Hellinger distance" by J. Oosterhoff and W.R....
Aug22-14 12:13 AM
2 185
Hi all, I am trying to construct a continuous matrix-valued function h=h(f,g) ; f,g in C^1,all defined in an open...
Aug14-14 10:35 PM
4 559
Recently I came across this information: \text{S1} = 1+1+1+1+\dotsb= -\frac{1}{2} \text{S2} = 1-1+1-1+\dotsb=...
Aug13-14 03:32 PM
1 238
We know that the derivative of the general Schwartz - Christoffel map (function) is: f'(z) = λ(z -...
Aug13-14 11:19 AM
2 1,416
Hello. I'm wondering if anyone has a table of transforms showing the result of an Abel transform on a Gaussian...
Aug11-14 10:45 AM
Mr Boom
1 271
Just as we have orthogonal vectors/vector spaces/etc., we can have orthogonal functions/function spaces/etc. I'm...
Aug10-14 09:45 PM
17 462
The Problem Let x and y be real numbers such that y<x, using the Dedekind cut construction of reals prove that...
Aug9-14 06:40 PM
5 326
I'm trying to understand Čech cohomology and for this I'm looking at the example of ##S^1## defined as ##/\sim## with...
Aug7-14 12:05 AM
2 1,580
I am trying to reconcile the following statement: " ||u||<=eps*||f|| means ||u||=O(eps) ("||u|| is order eps")... "...
Aug4-14 11:58 PM
Simon Bridge
7 304
Consider the sets ##X:= \{x\in\mathbb R^2: \enspace ||x-(-1,0)||_2 \leq 1\}## (a ball) and ##Y:=co\{(0,-1), (0,1),...
Aug4-14 10:34 PM
2 208
Are plane and surface of sphere different metric spaces? Can distance function of plane be applied as distance...
Aug2-14 09:00 PM
6 348

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