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.
Graduate Gaps In The System of Rational Numbers
  • · Replies 29 ·
Replies
29
Views
6K
Graduate Symplectic And Contact Manifolds
  • · Replies 15 ·
Replies
15
Views
2K
MHB Every Cauchy sequence converges
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Are All Manifolds Defined to Be Hausdorff?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate General Theorems on Bounding Manifolds?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Norm in R^d with Lebesgue measure
  • · Replies 9 ·
Replies
9
Views
2K
MHB Is the Fourier Transform of an L1 Function Always Continuous and Bounded?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Show Inclusion of Measures: Hölder's Inequality
  • · Replies 1 ·
Replies
1
Views
1K
MHB Show that it is metric and the measurable is 0
  • · Replies 11 ·
Replies
11
Views
3K
MHB Does the limit of $||f||_p$ equal $||f||_{\infty}$ as $p$ approaches infinity?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Showing Connexity of $f(K)$ for Continuous $f$ on Connexe $K$
  • · Replies 2 ·
Replies
2
Views
1K
MHB Assume the Limit Exists: Proving an Impossibility
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Functional Analysis vs. Complex Analysis?
  • · Replies 5 ·
Replies
5
Views
5K
MHB Is the Function Phi Lipschitz for Lebesgue Measurable Sets?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is a Subset of the Eigenvector Matrix in PCA Equivalent to a Submanifold?
  • · Replies 15 ·
Replies
15
Views
2K
MHB Get a Detailed Proof of Stirling's Formula
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Question about Riemann Zeta Function
  • · Replies 2 ·
Replies
2
Views
2K
MHB Does Compactness Ensure a Positive Minimum for Continuous Functions?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is the contradiction in the proof of Hahn Decomposition Theorem?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Considering the criterion for limit proofs
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Is Notation Impacting Measurability in Tonelli/Fubini's Theorem?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Show that there is a continuous g with compact support
  • · Replies 1 ·
Replies
1
Views
2K
MHB Prove Inequality: Nonnegative Reals {x}_{1}...{x}_{n} Sum to 1
  • · Replies 1 ·
Replies
1
Views
2K
MHB What is the objective of proving the limit for max and min?
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Continuity of an arc in the complex plane
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Eigenvectors of Fourier transform operator #F:L^2\to L^2#
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Quotient space of the unit sphere
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Harmonic Functions: Laplace's Equations & Analytic Functions
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Allowed values for the "differentiability limit" in complex analysis
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Analyticity of the complex logarithm on the negative real axis
  • · Replies 4 ·
Replies
4
Views
10K
MHB Proving ||u||_d = 0 and u=0 in Metric Spaces
  • · Replies 3 ·
Replies
3
Views
4K
MHB Laurent series, integral of a holomorphic function
  • · Replies 2 ·
Replies
2
Views
2K
MHB Analysis question involving Supremums and Infimums.
  • · Replies 3 ·
Replies
3
Views
2K
MHB Can you check my proof for a limit formula
  • · Replies 1 ·
Replies
1
Views
2K
MHB Linear Continuous AE(u): Unique Solution for Functional Analysis Problem
  • · Replies 2 ·
Replies
2
Views
2K
MHB How Does Subtracting a Limit Value Affect Convergence?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Concept of contour integration and integration along a square
  • · Replies 27 ·
Replies
27
Views
8K
MHB Proof of the Irrationality of e - attributed to Joseph Fourier
  • · Replies 2 ·
Replies
2
Views
2K
Graduate More Complex Analysis studying recommendations
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Identical Fourier coefficients of continuous ##f,\varphi\Rightarrow f=\varphi##
  • · Replies 2 ·
Replies
2
Views
2K
MHB What are the real and imaginary parts of z in terms of w?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Tough limit proof for a general f(x) and g(x)
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Representing a function of one variable in terms of a sequence of gaussians
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Convergence Criteria for Box Topology on R^ω
  • · Replies 2 ·
Replies
2
Views
2K
MHB Proving an Odd Function: ln(x+√(1+x²))
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the proof that the limit of a Cauchy sequence of integers is an integer?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Approximating simple function in $L_1$ with countable base
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Does (-2)^(⅔) have an imaginary component?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Special Properties of Hilbert Spaces?
  • · Replies 33 ·
2
Replies
33
Views
6K
Graduate Non-homeomorphis between CP^4 and CP^2 x CP^2
  • · Replies 4 ·
Replies
4
Views
1K
MHB What Does Norm Convergence Mean in $L^p$ Spaces?
  • · Replies 3 ·
Replies
3
Views
3K
MHB On integration, measurability, almost everywhere concept
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Approximation of ##f\in L_p## with simple function ##f_n\in L_p##
  • · Replies 6 ·
Replies
6
Views
2K
MHB How Can We Generalize Lebesgue Measurable Functions in Higher Dimensions?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Complex analysis: residue integration question
  • · Replies 7 ·
Replies
7
Views
3K
MHB What is this theorem about measurable functions saying?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Why do the reals fill the rationals with the absolute value?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Every sequence has a convergent subsequence?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Definition of boundary, Stokes' theorem
  • · Replies 6 ·
Replies
6
Views
2K
MHB Proving Parseval's Theorem for Schwartz Functions with Compact Support
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why don't these open set axioms specify that the empty set is open?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Prove √a(n) Converges to 0 | Stuck on Proof
  • · Replies 3 ·
Replies
3
Views
2K
MHB Lim of Convolution: Fourier Analysis Solution
  • · Replies 4 ·
Replies
4
Views
2K
MHB Is it enough to show that it is a Lebesgue measure?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Prove $\displaystyle \lim_{x \to 0}\frac{x}{1 + \sin^2(x)} = 0$
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Fourier transform of function of a complex variable
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Lowest coefficient of the i part of Riemann exponents
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Abuse of notation in relative homology theory
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Every bounded sequence is Cauchy?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Is the Real Number Line Actually Infinite?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Are Complex Analysis and Complex Variables the same thing?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Other names for the domain and range-straightening theorems?
  • · Replies 2 ·
Replies
2
Views
4K
MHB Is Swapping Limits and Integrals Justified in Complex Analysis?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Cauchy Sequences: What it Means to be $|x_{n+1}-x_n|_p< \epsilon$
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Is F continuous if it is both upper and lower semicontinuous?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate A misunderstanding of compact sets
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Explaining Electroweak Theory Decomposition to a Beginner
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Measurability and Lebesgue integral of complex functions
  • · Replies 4 ·
Replies
4
Views
2K
MHB Proving an Infinite $\sigma-$Algebra is Uncountable
  • · Replies 3 ·
Replies
3
Views
3K
MHB Find a subset of the real numbers
  • · Replies 7 ·
Replies
7
Views
2K
MHB How to Calculate $\int_0 ^{\infty} \sin t^2$ Using Complex Analysis?
  • · Replies 21 ·
Replies
21
Views
5K
Graduate Finding the Normal Cone of a Closed Convex Subset in a Hilbert Space
  • · Replies 5 ·
Replies
5
Views
1K
MHB Why Is a Rectangle Considered Closed and Bounded in Volume Proofs?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Proving the Zero Lebesgue Measure of Continuous Real Functions: Guidance Needed
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Two conditions of existence for Lebesgue integral
  • · Replies 2 ·
Replies
2
Views
2K
MHB The rectangle has an empty interior
  • · Replies 15 ·
Replies
15
Views
4K
MHB Measure Union of n Measurable Sets: Formula & Examples
  • · Replies 3 ·
Replies
3
Views
2K
MHB Show that the measure is equal to zero
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Can I get some examples of a function with following properies
  • · Replies 14 ·
Replies
14
Views
5K
Undergrad Why is preferable the line integral than the area integral over C plan
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Conformal Mapping: Transforming Polygons to Circles?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Complex Analysis: Learning Resources and Practice Problems
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Complements of Curves in Closed Surfaces: Homeomorphic?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Why is $w_p(x+y) \geq m$ and not $w_p(x+y) = m$ for $x,y \in \mathbb{Q}_p$?
  • · Replies 5 ·
Replies
5
Views
3K
MHB Question about minimum function and limit definition (proper)
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Prove Complex Numbers Triangle Inequality: lz-wl>=llzl-lwll
  • · Replies 1 ·
Replies
1
Views
1K
Graduate How to derive the branch cuts for complex arcsin(z)
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Staying Awake & Interested in Math Analysis Class
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Rademacher's Theorem: Introduction to Lipschitz Continuity
  • · Replies 1 ·
Replies
1
Views
2K
MHB How Does the Axiom of Archimedes Prove Integer Density in Real Numbers?
  • · Replies 3 ·
Replies
3
Views
2K