Topology and Analysis Forum

Post thread
Participate in expert discussion on topology and analysis topics. This includes point-set topology, Real, complex, harmonic and functional analysis. Also measure and integration theory.
Interpreting ##\alpha \delta(x)##: Is ##\alpha## at ##x=0##?
  • · Replies 1 ·
Replies
1
Views
2K
How Can Abelian Integrals Be Simplified for Beginners?
  • · Replies 6 ·
Replies
6
Views
4K
MHB Problem 15 section 5.1 from Bartle
  • · Replies 6 ·
Replies
6
Views
4K
Proving Element In Union of Two Infinite Sets Not Necessarily In Intersection
  • · Replies 3 ·
Replies
3
Views
2K
Does the Integral of a Derivative Equal the Function's Net Change?
  • · Replies 29 ·
Replies
29
Views
6K
What are upper and lower bounds and why are they important in mathematics?
  • · Replies 12 ·
Replies
12
Views
4K
Proving a conjecture in complex analysis
  • · Replies 2 ·
Replies
2
Views
2K
A good introductory book on real analysis with examples
  • · Replies 5 ·
Replies
5
Views
4K
Measure theory question on integrals.
  • · Replies 5 ·
Replies
5
Views
2K
MHB Compute Integrals: Integrate (z^3-6z^2+4)dz from -1+i to 1
  • · Replies 3 ·
Replies
3
Views
2K
MHB Analytic Function I: Proving f(z)=log z Not Analytic on Domain D w/ γ
  • · Replies 3 ·
Replies
3
Views
2K
MHB Analytic Function II: Complex Calculation
  • · Replies 3 ·
Replies
3
Views
2K
Bijections and need of zorn's lemma
  • · Replies 2 ·
Replies
2
Views
2K
How Does the Lax-Milgram Theorem Utilize Continuity and Coercivity?
  • · Replies 2 ·
Replies
2
Views
4K
MHB Nonstandard Analysis: Completeness of R via Every Limited Hyperreal
  • · Replies 3 ·
Replies
3
Views
2K
Proof Writing for Dummies: Intersection & Union Elements
  • · Replies 3 ·
Replies
3
Views
2K
Infinite Unions of Open/Closed Sets: Explained
  • · Replies 3 ·
Replies
3
Views
3K
Question about finite dimensional real l^p space
  • · Replies 2 ·
Replies
2
Views
2K
On an intuitive level, density/countability of Q
  • · Replies 3 ·
Replies
3
Views
4K
Q* (the set of rational cuts) has least upper bound property or not?
  • · Replies 2 ·
Replies
2
Views
3K
MHB Proving H is Complete & a Hilbert Space: Analysis of $\|.\|_H$
  • · Replies 5 ·
Replies
5
Views
3K
Proof about a limit property clarification
  • · Replies 4 ·
Replies
4
Views
2K
Is f(x) a Contraction Mapping?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Proving continuity with sequences
  • · Replies 7 ·
Replies
7
Views
2K
Fourier Series/transform and eigenvalues
  • · Replies 8 ·
Replies
8
Views
4K
MHB Proving Definition of Continuous Function: Hi, Carla!
  • · Replies 10 ·
Replies
10
Views
4K
Natural examples of metrics that are not Translation invariant.
  • · Replies 1 ·
Replies
1
Views
5K
Can Dehn Twists Be Applied to Non-Orientable Manifolds Like the Moebius Strip?
  • · Replies 4 ·
Replies
4
Views
3K
The Cartesian product theorem for dimension 0
  • · Replies 2 ·
Replies
2
Views
2K
Laurent series - where does f(z) need to be holomorphic?
  • · Replies 2 ·
Replies
2
Views
2K
Proof of Continuity of $x^n$ from Pugh's "Real Mathematical Analysis" Chapter 1
  • · Replies 5 ·
Replies
5
Views
3K
Calculating the density of optimally packed spheres
  • · Replies 4 ·
Replies
4
Views
3K
I proving something about my sequence
  • · Replies 2 ·
Replies
2
Views
2K
Are the Irrationals and Product Spaces Non-Homeomorphic?
  • · Replies 8 ·
Replies
8
Views
2K
Quick Chebychev Inequality Question
  • · Replies 14 ·
Replies
14
Views
2K
Real analysis epsilon delta problem
  • · Replies 1 ·
Replies
1
Views
2K
Direct proof by using if then technique
  • · Replies 10 ·
Replies
10
Views
6K
Real Analysis: Understanding Proof with Equations 3 & 4
  • · Replies 7 ·
Replies
7
Views
2K
Topology problem about Hausdorff space and compactness
  • · Replies 20 ·
Replies
20
Views
4K
Can We Show Y=X If Y is a Subspace of X and Y^c is First Category?”
  • · Replies 1 ·
Replies
1
Views
2K
Is Every Continuous Function on an Unbounded Set Uniformly Continuous?
  • · Replies 8 ·
Replies
8
Views
3K
Bilinear mappings, tensor products and p-summing operators
  • · Replies 4 ·
Replies
4
Views
2K
Construct uncountably dense and holes everywhere
  • · Replies 8 ·
Replies
8
Views
3K
MHB Measurable Function (Another Question)
  • · Replies 3 ·
Replies
3
Views
2K
MHB Measurable Function Composition: f∘g
  • · Replies 3 ·
Replies
3
Views
2K
MHB Proving Null Sets: Lebesgue Measure and Lipschitz Functions
  • · Replies 4 ·
Replies
4
Views
2K
What is the Significance of Completely Regular Spaces?
  • · Replies 125 ·
5
Replies
125
Views
21K
Topology of punctured plane vs topology of circle?
  • · Replies 4 ·
Replies
4
Views
4K
What Is the Hausdorff Dimension of \(\mathbb{Y}\)?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Can improper integrals converge without absolute convergence?
  • · Replies 7 ·
Replies
7
Views
2K
Equation of a line in complex plane
  • · Replies 3 ·
Replies
3
Views
4K
MHB Does the integral \int^{\infty}_{0} \frac{\log(t) \sin(t) }{t} \, dt converge?
  • · Replies 2 ·
Replies
2
Views
2K
Confusion with Disconnected sets
  • · Replies 3 ·
Replies
3
Views
2K
MHB Can Gauss Curvature Be Zero on a Genus 2 Surface?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Continuous Example: Weierstrass Function
  • · Replies 2 ·
Replies
2
Views
2K
Proving a sequence diverges directly
  • · Replies 2 ·
Replies
2
Views
2K
MHB Proving Lower Bound of $\int_{0}^{ \pi}\sin^{7}(x) \, dx$ is $(\pi/2)^7$
  • · Replies 2 ·
Replies
2
Views
2K
Scenarios where the Cauchy-Riemann equations aren't true?
  • · Replies 3 ·
Replies
3
Views
2K
MHB How Do You Differentiate the Modulus of a Complex Number in Riemannian Metrics?
  • · Replies 2 ·
Replies
2
Views
2K
Proving V is a Vector Space: Simplifying the Process with Axiom Lemma
  • · Replies 3 ·
Replies
3
Views
2K
Show L^p(E) is separable for any measurable E.
  • · Replies 4 ·
Replies
4
Views
2K
MHB Troubling contradiction in Functional Analysis
  • · Replies 1 ·
Replies
1
Views
2K
MHB Homeomorphism Between Q and Unit Sphere in R^3
  • · Replies 9 ·
Replies
9
Views
2K
Rudin's explanation of how rapid the series 1/(n) converges
  • · Replies 3 ·
Replies
3
Views
2K
Spectrum of a linear operator on a Banach space
  • · Replies 1 ·
Replies
1
Views
2K
MHB Optimizing Least Square Method for Ill-Conditioned Linear Problems
  • · Replies 8 ·
Replies
8
Views
2K
How intuitive is the idea of completeness?
  • · Replies 20 ·
Replies
20
Views
3K
Proof: Complex entire function bounded by a monomial is a polynomial
  • · Replies 1 ·
Replies
1
Views
3K
MHB Borel and σ-algebra related question
  • · Replies 1 ·
Replies
1
Views
2K
How to do circular curve fitting?
  • · Replies 2 ·
Replies
2
Views
3K
What Does F >= g Mean in a Function Definition?
  • · Replies 2 ·
Replies
2
Views
2K
Understanding the Algebra of Branch Cuts in Multi-Valued Functions
  • · Replies 3 ·
Replies
3
Views
3K
Can This Knot Be Identified from Knot Theory?
  • · Replies 1 ·
Replies
1
Views
2K
Can All Smooth Functions Near Zero Be Expressed by This Double Series?
  • · Replies 1 ·
Replies
1
Views
2K
Seperable + What Implies Second Countable?
  • · Replies 6 ·
Replies
6
Views
5K
MHB How is √2 μ Interpreted Geometrically?
  • · Replies 3 ·
Replies
3
Views
2K
Help understanding equivalent definitions for continuity
  • · Replies 2 ·
Replies
2
Views
2K
How can a Lissajous Curve be represented in 3D?
  • · Replies 3 ·
Replies
3
Views
4K
Ker[cos(x)] Analysis: \pi \mathbb{Z} ± π/2
  • · Replies 2 ·
Replies
2
Views
2K
Why Did Rudin Use Absolute Value When Calculating the Derivative?
  • · Replies 4 ·
Replies
4
Views
3K
Bernoulli's Rule: Existence of a Point c in (a,b)
  • · Replies 2 ·
Replies
2
Views
2K
Rudin Proof of Liouville Theorem (Complex A.)
  • · Replies 3 ·
Replies
3
Views
3K
Can an additive function be nonlinear without AC?
  • · Replies 5 ·
Replies
5
Views
4K
Vector Calculus by Marsden and Tromba vs. Vector Analysis by Brand
  • · Replies 2 ·
Replies
2
Views
4K
MHB Wedge product and change of variables
  • · Replies 1 ·
Replies
1
Views
2K
Given a metric space (X,d), the set X is open in X. HELP
  • · Replies 5 ·
Replies
5
Views
2K
MHB Bounded linear functional question? Real Analysis
  • · Replies 3 ·
Replies
3
Views
2K
What Are the Merits of the Laplace Transform?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Fixed point for a complex mapping.
  • · Replies 1 ·
Replies
1
Views
3K
MHB 3 questions about iterated integral
  • · Replies 2 ·
Replies
2
Views
2K
MHB Calculating an integral norm in L2
  • · Replies 1 ·
Replies
1
Views
5K
MHB What is the Countable Union of Countable Sets?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Looking for a Problem Book in Real Analysis?
  • · Replies 10 ·
Replies
10
Views
5K
Function Spaces C^k: Understanding Facts
  • · Replies 3 ·
Replies
3
Views
2K
MHB How Can Fourier Coefficients Help Solve Infinite Series Problems?
  • · Replies 9 ·
Replies
9
Views
3K
Questions about Derivatives and Continuity.
  • · Replies 5 ·
Replies
5
Views
2K
Role of real & functional analysis in physics?
  • · Replies 13 ·
Replies
13
Views
12K
MHB What is the Explanation for the Intermediate Value Theorem 2 Proof?
  • · Replies 2 ·
Replies
2
Views
2K
Recommend book to follow Introduction to Analysis by Rosenlicht
  • · Replies 2 ·
Replies
2
Views
3K
MHB Prove Zeros & Poles of Meromorphic Function Have No Limit Point
  • · Replies 2 ·
Replies
2
Views
2K