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.
Undergrad Supremum Property (AoC) .... etc .... Another question/Issue
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Help with expression ##F(it)-F(-it)## in the Abel-Plana form
  • · Replies 1 ·
Replies
1
Views
2K
MHB The Completeness Axiom .... and Sohrab Exercise 2.1.29 ....
  • · Replies 6 ·
Replies
6
Views
2K
MHB Struggling with Exercise 2.1.40 in Sohrab's Basic Real Analysis?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Density of Q in R .... Sohrab Theorem 2.1.38 ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB The AM-GM Inequality - Sohrab Proposition 2.1.25 ....
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad The AM-GM Inequality - Sohrab Proposition 2.1.25 ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Proof of Cauchy's Inequality .... Sohrab Proposition 2.1.23 ....
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Can a tetrahedron have all dihedral angles rational?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Differentiating a particular integral (retarded potential)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Integers as an Ordered Integral Domain .... Bloch Th. 1.4.6
  • · Replies 7 ·
Replies
7
Views
2K
High School Knot theory: closed loops in n dimensions
  • · Replies 3 ·
Replies
3
Views
2K
MHB The Integers as an Ordered Integral Domain .... Bloch Theorem 1.4.6 ....
  • · Replies 4 ·
Replies
4
Views
2K
MHB Some Properties of the Rational Numbers .... Bloch Exercise 1.5.9 (3)
  • · Replies 2 ·
Replies
2
Views
2K
MHB Sum of a rational number and an irrational number ....
  • · Replies 3 ·
Replies
3
Views
2K
MHB The Set of Positive Integers as a Copy of the Natural Numbers ....
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Homotopy Definitions: Homeomorphisms, Homotopies & Retracts
  • · Replies 13 ·
Replies
13
Views
3K
Graduate Parameterizing the 3-Sphere: 3 Angles?
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad The Set of Positive Integers - a Copy of the Natural Numbers
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad The Well-Ordering Principle for the Natural Numbers ....
  • · Replies 3 ·
Replies
3
Views
4K
MHB The Well-Ordering Principle for the Natural Numbers
  • · Replies 2 ·
Replies
2
Views
2K
MHB Properties of "less Than" & "Less Than or Equals" - Bloch Theorem 1.2.9 - Peter
  • · Replies 3 ·
Replies
3
Views
1K
MHB Addition and Multiplication of Natural Numbers - Bloch Th. 1.2.7 .... ....
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Properties of 'less than" and "less than or equals"
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Addition/Multiplication of Natural Numbers - Bloch Th. 1.2.7
  • · Replies 4 ·
Replies
4
Views
2K
High School How Does Group Orbit Theory Relate Torus and Cylinder Structures?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Proving non homeomorphism between a closed interval & ##\mathbb{R}##
  • · Replies 45 ·
2
Replies
45
Views
7K
Graduate Is This the Correct Way to Attach Möbius Strips to a Torus?
  • · Replies 12 ·
Replies
12
Views
5K
Undergrad Differentiation under the integral in retarded potentials
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad How to show that a 4-polytope is a tiling of the 3-sphere
  • · Replies 4 ·
Replies
4
Views
2K
High School Preferred directions on a torus?
  • · Replies 8 ·
Replies
8
Views
2K
High School Uniqueness of Analytic Functions
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Solving Complex Integral Paths - Real Line Poles
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Laplacian of Retarded Potential: How to Derive the Equation Mathematically?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Integration of Legendre Polynomials with different arguments
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Difference between holomoprhic and analytic functions
  • · Replies 19 ·
Replies
19
Views
7K
Undergrad Is it possible to prove that the circle is a manifold using open spheres?
  • · Replies 29 ·
Replies
29
Views
6K
Graduate Half-face traversal on general polyhedra
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Merging Two Threads: Complex Integrals & Branch Cuts
  • · Replies 5 ·
Replies
5
Views
2K
High School Real Analysis: Expanding a Function at Different Points
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Understanding Isolated Singularities in the Residue Theorem
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Is the Unit Closed Disk Minus the Origin Homeomorphic to the Unit Circle?
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad What Makes the Jordan Curve Theorem a Cornerstone of Topology?
  • · Replies 21 ·
Replies
21
Views
3K
Undergrad Identical zero function in the complex plane
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Limitations of the Lebesgue Integral
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Difference between complex and real analysis
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Pointwise and Uniform Convergence
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Cauchy's Theorem: Understanding Complex Analysis
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Proof of Harmonic Function Infinitely Differentiable
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Boundary and homeomorphism
  • · Replies 54 ·
2
Replies
54
Views
7K
Undergrad Learning Complex Integration: Endpoints & Paths
  • · Replies 2 ·
Replies
2
Views
1K
MHB Power series and uniform convergence.
  • · Replies 1 ·
Replies
1
Views
2K
MHB Proving expression is always positive
  • · Replies 2 ·
Replies
2
Views
3K
MHB Z²+bz+1=0, where |b|≤2. For which values of b do the following hold?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Why do we have fast convergence?
  • · Replies 3 ·
Replies
3
Views
2K
High School Stereographic projection and uneven scaling
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Mapping double cover over a torus
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Dirac Delta and Residue Calculus
  • · Replies 3 ·
Replies
3
Views
3K
MHB Sine fourier series with period 1
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Do these manifolds have a boundary?
  • · Replies 26 ·
Replies
26
Views
4K
MHB Find cosine series: Period 4 for f(x)
  • · Replies 16 ·
Replies
16
Views
3K
MHB How to prove such value for a derivative?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Proving Urysohn's Lemma: Normal vs Perfectly Normal Spaces
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Is a game situation in chess topologically invariant?
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Does Sobolev Space Boundedness Relate to Different Norms in $R^n$?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Need help, are these functions differentiable?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Homology groups with points identified
  • · Replies 21 ·
Replies
21
Views
4K
MHB Series Convergence: Ratio Test & Lim. n→∞
  • · Replies 2 ·
Replies
2
Views
2K
High School S u p x i n [ a , b ] | P n ( x ) − f ( x ) | < ϵ
  • · Replies 5 ·
Replies
5
Views
1K
MHB Proving an Integral with a Direct Proof & Epsilon Argument
  • · Replies 12 ·
Replies
12
Views
3K
MHB Real Analysis - Prove the Riemann Integral Converges
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Wrong proofs of Riemann hypothesis
  • · Replies 1 ·
Replies
1
Views
2K
MHB The parameter λ in linear integral equations
  • · Replies 2 ·
Replies
2
Views
1K
MHB Real Analysis - Riemann Integral Proof
  • · Replies 4 ·
Replies
4
Views
2K
MHB Proving Limits: How to Show x^x Approaches Infinity as x Approaches Infinity?
  • · Replies 4 ·
Replies
4
Views
1K
MHB How Do You Find the Limit of (e^x - 1) / Sin(x) as x Approaches 0?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate A pasting lemma counterexample (of sorts)
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Homotopy Equivalence: Definition & Examples
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Is this function in the L^2(0,1) space for certain values of C_1 and C_2?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate What Conditions Determine a Zero Measure Set in Fourier Transforms?
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Proving Injectivity and Surjectivity: A Fundamental Concept in Function Theory
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Definition of Topology - What Does {##U_\alpha | \alpha \in I##} Mean?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Is there an on-line table of genus of algebraic functions?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How does the angle γ change under inversion in Euler angles?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Understanding the Definition of Boundary in Set Theory for Topological Spaces
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What defines a large gauge transformation, really?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Difference between tensor and vector?
  • · Replies 2 ·
Replies
2
Views
2K
What Does 'Canonical' Mean in a Mathematical Context?
  • · Replies 3 ·
Replies
3
Views
3K
MHB What is [2x] Notation? Continuity Question
  • · Replies 3 ·
Replies
3
Views
2K
MHB Proving Continuity at a Point with Non-Zero Value: A Case Study
  • · Replies 4 ·
Replies
4
Views
2K
MHB Has anybody seen this looks kind double Mittag-Leffler
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad For direct proof, how do you choose M for bounded sequence?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Understanding Dedekind Cuts: How to Recognize a Cut
  • · Replies 2 ·
Replies
2
Views
2K
MHB Why is the solution to the Volterra integral equation written as a power series?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Convergence of Integrals: Exploring Methods and Challenges
  • · Replies 11 ·
Replies
11
Views
3K
MHB How Do We Determine the Convergence of These Complex Integrals?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Laplace transform of a series in time t
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Can 2D Vector Subspaces Form 3D Surfaces and How to Find Their Intersection?
  • · Replies 16 ·
Replies
16
Views
2K
MHB Understanding the Completeness Axiom: A Discussion on Ross' Analysis
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Implicit function parameterization
  • · Replies 16 ·
Replies
16
Views
3K