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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Threads

Undergrad Is S^2 - {N} Homeomorphic to R^2?

  • PsychonautQQ
  • · Replies 3 ·
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3

Using Residue Theorem To Prove Value Of Summation

  • joypav
  • · Replies 4 ·
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4

Undergrad Euler Characteristic of the Projective plane and sphere?

  • PsychonautQQ
  • · Replies 3 ·
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3

Undergrad What is an atlas for a torus manifold?

  • aheight
  • · Replies 4 ·
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4

Theorem 1.8: Sets or Domains in the Complex Plane - Palka Ch.2

  • Math Amateur
  • · Replies 3 ·
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3

Why Does γ(t) = z(1-t) Represent the Same Curve in Reverse?

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Homotopy Class vs Fundamental Group.

  • FallenApple
  • · Replies 6 ·
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6

Graduate Is the Long Line Locally Euclidean, Hausdorff, and Path Connected?

  • PsychonautQQ
  • · Replies 3 ·
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3

Another Question On B&S, Theorem 7.3.5 - Fundamental Theorem Of Calculus ...

  • Math Amateur
  • · Replies 2 ·
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2

Fundamental Theorem Of Calculus (Second Form) - B&S Theorem 7.3.5 .... ....

  • Math Amateur
  • · Replies 2 ·
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2

Convergence in topological space

  • Julio1
  • · Replies 2 ·
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2

Riemann Integration - The Additivity Theorem .... B&S Theorem 7.2.9 ....

  • Math Amateur
  • · Replies 1 ·
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1

Limit Superior .... B&S Therem 3.4.11 .... ....

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Proving Convergence: Solving the Limit of 1/(6n^2+1) = 0

  • Mr Davis 97
  • · Replies 8 ·
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8

Undergrad How can we characterize mathematical analysis?

  • Mr Davis 97
  • · Replies 2 ·
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2

Undergrad How Does the Supremum of -A Relate to Its Elements?

  • Mr Davis 97
  • · Replies 5 ·
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5

Remarks on Limit Superrior .... B&S Page 82 .... Example ....

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Hahn-Banach From Systems of Linear Equations

  • bolbteppa
  • · Replies 9 ·
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9

High School Complex numbers imaginary part

  • MikeSv
  • · Replies 11 ·
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11

Undergrad Proving that square root of 2 exists

  • Mr Davis 97
  • · Replies 16 ·
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16

Undergrad Irreducible representation of SU(2)

  • davidge
  • · Replies 3 ·
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3

Undergrad Noncompact locally compact Hausdorff continuous mapping

  • PsychonautQQ
  • · Replies 14 ·
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14

Undergrad Continuity of the determinant function

  • dextercioby
  • · Replies 1 ·
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1

Undergrad Can a Topological Space be Both a 1-Manifold and an n-Manifold?

  • PsychonautQQ
  • · Replies 17 ·
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17

Undergrad Generalization of measure theory to uncountable unions

  • greypilgrim
  • · Replies 5 ·
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5

L'Hospital's Rule .... Bartle and Sherbert Theorem 6.2.3 .... ....

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Complex Conjugates: Replacing i & Taking Alpha's Conjugate?

  • dyn
  • · Replies 20 ·
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20

What is the connection between sin and cos in Example 6.3.4?

  • Math Amateur
  • · Replies 2 ·
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2

Understanding Corollary 6.2.2 of B&S Theorem 6.2.1

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad Corollary to the Interior Extremum Theorem .... ....

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Is e: [0,1] --> S^1 a Quotient Map?

  • PsychonautQQ
  • · Replies 3 ·
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3

Undergrad Does L_g pass to the quotient G/H?

  • PsychonautQQ
  • · Replies 4 ·
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4

Undergrad What Is a Non-Linear Ordered Set?

  • Silviu
  • · Replies 1 ·
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1

Undergrad Is R_d x R Locally Euclidean of Dimension 1?

  • PsychonautQQ
  • · Replies 1 ·
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1

Chain Rule - B&S Theorem 6.1.6 ....

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Gluing lemma / infinite corollary

  • PsychonautQQ
  • · Replies 6 ·
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6

Undergrad Contort rectangle to torus minus splice=homomorphism?

  • aheight
  • · Replies 1 ·
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1

Undergrad Why is this line not homeomorphic to the unit circle?

  • Mr Davis 97
  • · Replies 10 ·
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10

Undergrad Limits and Continuity - Absolute Value Technicality ....

  • Math Amateur
  • · Replies 2 ·
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2
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1

Lipschitz Condition and Uniform Continuity

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Relation of completeness to the l.u.b. property?

  • Mr Davis 97
  • · Replies 5 ·
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5

Continuous Functions on Intervals .... B&S Theorem 5.3.2 ....

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Square root of a complex number

  • Nipon Waiyaworn
  • · Replies 5 ·
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5

Continuous Functions - Thomae's Function ....

  • Math Amateur
  • · Replies 2 ·
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2

Proving the Sum of a Sequence Equals n Using Induction

  • joypav
  • · Replies 6 ·
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6

Undergrad Pole in Stereographic Projection

  • FallenApple
  • · Replies 1 ·
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1

Graduate Algebraic topology applied to Neuroscience

  • Auto-Didact
  • · Replies 2 ·
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2

Limits of Functions .... L&S Example 10.7 (2) ....

  • Math Amateur
  • · Replies 3 ·
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3

Limits of Functions .... B&S Theorem 4.2.9 .... ....

  • Math Amateur
  • · Replies 2 ·
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2

High School Understanding Extremum and Derivatives at Boundary Points

  • Leo Authersh
  • · Replies 4 ·
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4

High School Basic complex number math -- what am I doing wrong?

  • Isaac0427
  • · Replies 3 ·
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3

High School Graphical Representation of a Complex Sphere

  • Leo Authersh
  • · Replies 6 ·
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6

Undergrad Simplicial complex geometric realization 1-manifold

  • PsychonautQQ
  • · Replies 2 ·
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2

Limits and Continuity - Absolute Value Technicality ....

  • Math Amateur
  • · Replies 3 ·
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3

High School Does Every Set in the Axiom of Choice Include an Empty Set?

  • kidsasd987
  • · Replies 1 ·
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1

Limits of Sequences .... Bartle and Shebert, Example 3.4.3 (b) ....

  • Math Amateur
  • · Replies 6 ·
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6

Limits of Sequences .... Stoll Theorem 2.2.6

  • Math Amateur
  • · Replies 4 ·
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4

Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (1) ....

  • Math Amateur
  • · Replies 2 ·
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2

Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.12 ....

  • Math Amateur
  • · Replies 2 ·
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2

Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (b) ....

  • Math Amateur
  • · Replies 5 ·
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5

Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (c) ....

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Limits of Sequences .... Bartle & Shebert, Example 3.4.3 (b)

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad What does ".... is zero to order ...." mean?

  • Tomtam
  • · Replies 4 ·
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4

Undergrad Ascending subset sequence with axiom of choice

  • jostpuur
  • · Replies 3 ·
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3

Open Sets - Unions and Intersections -

  • Math Amateur
  • · Replies 8 ·
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8

Limits of Sequences .... Sohrab Exercise 2.2.7

  • Math Amateur
  • · Replies 3 ·
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3

How to use DeMoivre's theorem to find the product of complex numbers?

  • karush
  • · Replies 13 ·
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13

Closed Sets - Sohrab Exercise 2.2.4 - Part 2

  • Math Amateur
  • · Replies 3 ·
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3

Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Can a Circular Function with Complex Variable Represent a 3D Graph?

  • Leo Authersh
  • · Replies 7 ·
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7

Hcc8.11 change each to complex form and find product

  • karush
  • · Replies 3 ·
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3

Supremum Property (AoC) .... etc .... Yet a further question/Issue ....

  • Math Amateur
  • · Replies 2 ·
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2

Supremum Property (AoC) .... etc .... Another question/Issue ....

  • Math Amateur
  • · Replies 2 ·
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2

Supremum Property (AoC), Archimedean Property, Nested Intervals Theorem ....

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Hyperreal Convergence: Is It 0 or Infinitesimal?

  • Someone2841
  • · Replies 1 ·
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1

Undergrad Supremum Property (AoC) .... etc .... Yet a further question

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Can Complex Numbers Be Viewed as Real Numbers on the X and Y Plane?

  • Leo Authersh
  • · Replies 5 ·
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5

Undergrad Why Does the Cut of $\mathbb{Q}$ Correspond to $\sqrt{2}$?

  • Mr Davis 97
  • · Replies 3 ·
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3

Undergrad Supremum Property, Archimedean Property, Nested Intervals

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Supremum Property (AoC) .... etc .... Another question/Issue

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Help with expression ##F(it)-F(-it)## in the Abel-Plana form

  • JasonPhysicist
  • · Replies 1 ·
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1

The Completeness Axiom .... and Sohrab Exercise 2.1.29 ....

  • Math Amateur
  • · Replies 6 ·
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6

Struggling with Exercise 2.1.40 in Sohrab's Basic Real Analysis?

  • Math Amateur
  • · Replies 4 ·
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4

Density of Q in R .... Sohrab Theorem 2.1.38 ....

  • Math Amateur
  • · Replies 2 ·
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2

The AM-GM Inequality - Sohrab Proposition 2.1.25 ....

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad The AM-GM Inequality - Sohrab Proposition 2.1.25 ....

  • Math Amateur
  • · Replies 2 ·
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2

Proof of Cauchy's Inequality .... Sohrab Proposition 2.1.23 ....

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Can a tetrahedron have all dihedral angles rational?

  • Zafa Pi
  • · Replies 4 ·
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4

Undergrad Differentiating a particular integral (retarded potential)

  • DavideGenoa
  • · Replies 2 ·
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2

Undergrad Integers as an Ordered Integral Domain .... Bloch Th. 1.4.6

  • Math Amateur
  • · Replies 7 ·
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7

High School Knot theory: closed loops in n dimensions

  • DaveC426913
  • · Replies 3 ·
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3

The Integers as an Ordered Integral Domain .... Bloch Theorem 1.4.6 ....

  • Math Amateur
  • · Replies 4 ·
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4

Some Properties of the Rational Numbers .... Bloch Exercise 1.5.9 (3)

  • Math Amateur
  • · Replies 2 ·
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2

Sum of a rational number and an irrational number ....

  • Math Amateur
  • · Replies 3 ·
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3

The Set of Positive Integers as a Copy of the Natural Numbers ....

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Homotopy Definitions: Homeomorphisms, Homotopies & Retracts

  • Silviu
  • · Replies 13 ·
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13

Graduate Parameterizing the 3-Sphere: 3 Angles?

  • pcr
  • · Replies 15 ·
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15

Undergrad The Weierstrass function's' odd qualities

  • rumborak
  • · Replies 4 ·
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4

Undergrad The Set of Positive Integers - a Copy of the Natural Numbers

  • Math Amateur
  • · Replies 8 ·
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8