Topology and Analysis Forum

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.

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Undergrad The Well-Ordering Principle for the Natural Numbers ....

  • Math Amateur
  • · Replies 3 ·
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3

The Well-Ordering Principle for the Natural Numbers

  • Math Amateur
  • · Replies 2 ·
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2

Properties of "less Than" & "Less Than or Equals" - Bloch Theorem 1.2.9 - Peter

  • Math Amateur
  • · Replies 3 ·
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3

Addition and Multiplication of Natural Numbers - Bloch Th. 1.2.7 .... ....

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Properties of 'less than" and "less than or equals"

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Addition/Multiplication of Natural Numbers - Bloch Th. 1.2.7

  • Math Amateur
  • · Replies 4 ·
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4

High School How Does Group Orbit Theory Relate Torus and Cylinder Structures?

  • jackferry
  • · Replies 2 ·
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2

Undergrad Proving non homeomorphism between a closed interval & ##\mathbb{R}##

  • davidge
  • · Replies 45 ·
2
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45

Graduate Is This the Correct Way to Attach Möbius Strips to a Torus?

  • dkotschessaa
  • · Replies 12 ·
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12

Undergrad A question about the formal definition of limit

  • flamengo
  • · Replies 3 ·
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3

How to Avoid Extraneous Solutions in Solving Complex Equations

  • Yankel
  • · Replies 3 ·
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3

Undergrad Differentiation under the integral in retarded potentials

  • DavideGenoa
  • · Replies 4 ·
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4

Complex Numbers - from Polar to Algebraic

  • Yankel
  • · Replies 2 ·
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2

Undergrad How to show that a 4-polytope is a tiling of the 3-sphere

  • t_r_theta_phi
  • · Replies 4 ·
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4

Undergrad Is the Maximum of a Continuous Function Proven in This Content?

  • TomMat
  • · Replies 2 ·
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2

Undergrad Solve Scalar Product Problem in Set R of Functions [0,1]

  • Gear300
  • · Replies 3 ·
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3

Geometric Series with Complex Numbers

  • Yankel
  • · Replies 3 ·
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3

High School Preferred directions on a torus?

  • gerald V
  • · Replies 8 ·
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8

Polar Representation of a Complex Number

  • Yankel
  • · Replies 5 ·
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5

High School Uniqueness of Analytic Functions

  • jackferry
  • · Replies 16 ·
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16

Undergrad Solving Complex Integral Paths - Real Line Poles

  • Silviu
  • · Replies 4 ·
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4

Drawing Complex Numbers on a Plane

  • Yankel
  • · Replies 2 ·
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2

Undergrad The graph of sin inverse (sin x) after the domain of (- pi/2, pi/2)

  • esha
  • · Replies 5 ·
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5

Undergrad Laplacian of Retarded Potential: How to Derive the Equation Mathematically?

  • DavideGenoa
  • · Replies 4 ·
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4

Complex Numbers - Number of Solutions

  • Lancelot1
  • · Replies 3 ·
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3

Complex Numbers - writing in polar form

  • srg263
  • · Replies 15 ·
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15

Undergrad Closed surfaces and closed curves

  • flamengo
  • · Replies 2 ·
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2

Undergrad Integration of Legendre Polynomials with different arguments

  • Alan Sammarone
  • · Replies 1 ·
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1

Undergrad Difference between holomoprhic and analytic functions

  • Silviu
  • · Replies 19 ·
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19

Undergrad Is it possible to prove that the circle is a manifold using open spheres?

  • davidge
  • · Replies 29 ·
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29

Undergrad Constant raised to complex numbers

  • Mr Real
  • · Replies 14 ·
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14

Graduate Half-face traversal on general polyhedra

  • Estanho
  • · Replies 9 ·
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9

Undergrad Merging Two Threads: Complex Integrals & Branch Cuts

  • Silviu
  • · Replies 5 ·
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5

High School Real Analysis: Expanding a Function at Different Points

  • Silviu
  • · Replies 11 ·
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11

Undergrad Understanding Isolated Singularities in the Residue Theorem

  • Silviu
  • · Replies 7 ·
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7

Undergrad Is the Unit Closed Disk Minus the Origin Homeomorphic to the Unit Circle?

  • davidge
  • · Replies 17 ·
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17

Undergrad What Makes the Jordan Curve Theorem a Cornerstone of Topology?

  • Silviu
  • · Replies 21 ·
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21

Undergrad Identical zero function in the complex plane

  • Silviu
  • · Replies 5 ·
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5

Undergrad Limitations of the Lebesgue Integral

  • The_eToThe2iPi
  • · Replies 15 ·
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15

Finding Real Solutions for a Complex Equation

  • mathdad
  • · Replies 10 ·
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10

Undergrad Difference between complex and real analysis

  • Silviu
  • · Replies 11 ·
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11

Undergrad Pointwise and Uniform Convergence

  • Silviu
  • · Replies 5 ·
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5

Undergrad Cauchy's Theorem: Understanding Complex Analysis

  • Silviu
  • · Replies 7 ·
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7

Undergrad Proof of Harmonic Function Infinitely Differentiable

  • Silviu
  • · Replies 4 ·
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4

Undergrad Boundary and homeomorphism

  • davidge
  • · Replies 54 ·
2
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54

Undergrad Learning Complex Integration: Endpoints & Paths

  • Silviu
  • · Replies 2 ·
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2

Power series and uniform convergence.

  • MissC
  • · Replies 1 ·
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1

Undergrad Solving Ordinal Arithmetic: X Countably Compact but Not Compact

  • Gear300
  • · Replies 5 ·
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5

Proving expression is always positive

  • Carla1985
  • · Replies 2 ·
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Z²+bz+1=0, where |b|≤2. For which values of b do the following hold?

  • Stephen Safee
  • · Replies 6 ·
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6

Why do we have fast convergence?

  • evinda
  • · Replies 3 ·
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3

High School Dimension of subset containing two circles

  • RubinLicht
  • · Replies 4 ·
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4

High School Stereographic projection and uneven scaling

  • Tahmeed
  • · Replies 1 ·
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1

Undergrad Mapping double cover over a torus

  • aheight
  • · Replies 5 ·
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5

Graduate Dirac Delta and Residue Calculus

  • Daniel Gallimore
  • · Replies 3 ·
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3

Sine fourier series with period 1

  • evinda
  • · Replies 6 ·
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6

High School How Does the Unit Circle Relate to Euler's Formula in Complex Numbers?

  • MikeSv
  • · Replies 10 ·
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10

Undergrad Do these manifolds have a boundary?

  • davidge
  • · Replies 26 ·
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26

Find cosine series: Period 4 for f(x)

  • evinda
  • · Replies 16 ·
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16

High School Isn't the Riemann Hypothesis just a convention?

  • mustang19
  • · Replies 25 ·
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25

How to prove such value for a derivative?

  • FallArk
  • · Replies 9 ·
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9

Undergrad Proving Urysohn's Lemma: Normal vs Perfectly Normal Spaces

  • Gear300
  • · Replies 3 ·
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3

Undergrad Is a game situation in chess topologically invariant?

  • moriheru
  • · Replies 4 ·
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4

Undergrad Dimension using box counting technique

  • transmini
  • · Replies 3 ·
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3

How Does Sobolev Space Boundedness Relate to Different Norms in $R^n$?

  • Danny2
  • · Replies 4 ·
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4

Need help, are these functions differentiable?

  • FallArk
  • · Replies 4 ·
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4

Undergrad Why doesn't √-1×√-1 always equal 1 in complex numbers?

  • Gourav kumar Lakhera
  • · Replies 3 ·
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3

Graduate Homology groups with points identified

  • dkotschessaa
  • · Replies 21 ·
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21

Series Convergence: Ratio Test & Lim. n→∞

  • Confusedalways
  • · Replies 2 ·
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2

Undergrad Can Complex Numbers Be Ordered?

  • Arman777
  • · Replies 6 ·
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6

Undergrad Interesting question: why is ln(-1) in polar form....?

  • rabualeez
  • · Replies 1 ·
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1

High School S u p x i n [ a , b ] | P n ( x ) − f ( x ) | < ϵ

  • feerrr
  • · Replies 5 ·
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5

Prove: f(x) = 0 has infinitely many solutions

  • lfdahl
  • · Replies 2 ·
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2

Proving an Integral with a Direct Proof & Epsilon Argument

  • joypav
  • · Replies 12 ·
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12

Real Solutions for x in a Complex Equation

  • mathdad
  • · Replies 2 ·
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2

Real Analysis - Prove the Riemann Integral Converges

  • joypav
  • · Replies 7 ·
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7

Undergrad Wrong proofs of Riemann hypothesis

  • Silviu
  • · Replies 1 ·
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1

The parameter λ in linear integral equations

  • sarrah1
  • · Replies 2 ·
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2

Real Analysis - Riemann Integral Proof

  • joypav
  • · Replies 4 ·
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4
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4

Undergrad How to Prove the Partial Fraction Formula for Distinct Complex Numbers?

  • jostpuur
  • · Replies 2 ·
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2

How Do You Find the Limit of (e^x - 1) / Sin(x) as x Approaches 0?

  • FallArk
  • · Replies 3 ·
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3

Graduate A pasting lemma counterexample (of sorts)

  • dkotschessaa
  • · Replies 9 ·
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9

Undergrad Definition of the root of -1 for different roots

  • Mr Davis 97
  • · Replies 8 ·
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8

Undergrad Homotopy Equivalence: Definition & Examples

  • Silviu
  • · Replies 7 ·
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7

Graduate Is this function in the L^2(0,1) space for certain values of C_1 and C_2?

  • LagrangeEuler
  • · Replies 6 ·
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6

Graduate What Conditions Determine a Zero Measure Set in Fourier Transforms?

  • mnb96
  • · Replies 8 ·
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8

Undergrad Proving Injectivity and Surjectivity: A Fundamental Concept in Function Theory

  • tlkieu
  • · Replies 2 ·
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2

Undergrad Definition of Topology - What Does {##U_\alpha | \alpha \in I##} Mean?

  • Silviu
  • · Replies 4 ·
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4

Undergrad Is there an on-line table of genus of algebraic functions?

  • aheight
  • · Replies 2 ·
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2

Undergrad How does the angle γ change under inversion in Euler angles?

  • ftft
  • · Replies 2 ·
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2

Undergrad Understanding the Definition of Boundary in Set Theory for Topological Spaces

  • Silviu
  • · Replies 4 ·
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4

Graduate What defines a large gauge transformation, really?

  • jakob1111
  • · Replies 1 ·
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1

Undergrad Difference between tensor and vector?

  • Vitani11
  • · Replies 2 ·
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2

Undergrad Difference Analysis and Calculus

  • ItsTheSebbe
  • · Replies 5 ·
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5

Undergrad What Does 'Canonical' Mean in a Mathematical Context?

  • Flubertin
  • · Replies 3 ·
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3

What is [2x] Notation? Continuity Question

  • FallArk
  • · Replies 3 ·
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3

Proving Continuity at a Point with Non-Zero Value: A Case Study

  • FallArk
  • · Replies 4 ·
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4

Has anybody seen this looks kind double Mittag-Leffler

  • sarrah1
  • · Replies 1 ·
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1

Undergrad For direct proof, how do you choose M for bounded sequence?

  • mikeyBoy83
  • · Replies 12 ·
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12