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 Proof that retract of Hausdorff space is closed

  • PsychonautQQ
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1

Undergrad How Does Closure in a Neighborhood Imply Membership in a Set?

  • PsychonautQQ
  • · Replies 12 ·
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12

The Residue Theorem To Evaluate Integrals

  • joypav
  • · Replies 5 ·
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5

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

Limit notation in Bartle and Sherbert Theorem 7.3.5

  • Math Amateur
  • · Replies 2 ·
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2

Proof of Bartle and Sherbert Theorem 7.3.5 on the Riemann integral

  • 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 theorem 3.4.11 proof in Bartle and Sherbert

  • 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

Density theorem application to subsequential limits of rationals

  • 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 Proving every irreducible representation of SU(2) uses ladder operators

  • 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 proof in Bartle and Sherbert Theorem 6.3.3

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Conjugate of αe^(iα) when α is complex

  • dyn
  • · Replies 20 ·
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20

Why does sin x / √x equal cos x / (1/2√x)?

  • Math Amateur
  • · Replies 2 ·
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2

Proving Corollary 6.2.2 of Bartle and Sherbert Theorem 6.2.1

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad Interior Extremum Theorem corollary proof and continuity assumption

  • 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

Caratheodory's theorem in B&S chain rule proof

  • 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 Proving |x| < |p| + 1 from |x - p| < 1

  • 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

Why is f continuous at x in Bartle-Sherbert 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

Finite rationals with denominator less than n₀

  • 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

Why |x - 2| < 1/2 implies |x - 1| > 1/2

  • Math Amateur
  • · Replies 3 ·
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3

Bartle and Sherbert theorem 4.2.9: why f(x) > L/2 > 0?

  • 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 Why does |ψ|² give different results for fe^ikx + ge^ikx?

  • 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

Proving |x| < |p| + 1 from |x - p| < 1

  • 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

Proving z_n > 1 and z_(n+1) < z_n for z_n = c^(1/n)

  • 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

Sohrab exercise 2.1.12 part 1 on ordering of real numbers

  • Math Amateur
  • · Replies 2 ·
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2

Sohrab exercise 2.1.10(b): ordering on real numbers

  • Math Amateur
  • · Replies 5 ·
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5

Sohrab Exercise 2.1.10 (c): ordering on real numbers

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Show that c^(1/n) is decreasing and greater than 1

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad What does "zero to order" mean in analysis?

  • 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

Proving lim(1/(1+na))=0 using epsilon-delta definition

  • 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

Union of intervals [1/n, 1-1/n] equals (0,1) in Sohrab 2.2.4

  • Math Amateur
  • · Replies 3 ·
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3

Proving ℕ and ℤ are closed sets in ℝ

  • 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

Nested intervals theorem proof in Sohrab theorem 2.1.45

  • Math Amateur
  • · Replies 2 ·
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2

Theorem 2.1.45: supremum property and nested intervals

  • Math Amateur
  • · Replies 2 ·
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2

Theorem 2.1.45: supremum property and nested intervals theorem in Sohrab

  • 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 Nested intervals uniqueness proof in Sohrab theorem 2.1.45

  • 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 Sohrab theorem 2.1.45: nested intervals and kₙ₊₁ logic

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Branch cuts for F(it)-F(-it) where F(z)=√(z²+A²)

  • JasonPhysicist
  • · Replies 1 ·
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1

Sohrab Exercise 2.1.29 on equivalence of supremum and infimum properties

  • Math Amateur
  • · Replies 6 ·
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6

Corollary 2.1.39 and Exercise 2.1.40 in Sohrab's Basic Real Analysis

  • Math Amateur
  • · Replies 4 ·
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4

Why can we assume x > 0 in Sohrab's density of Q in R proof?

  • Math Amateur
  • · Replies 2 ·
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2

AM-GM inequality proof using strong induction in Sohrab 2.1.25

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Sohrab's proof of AM-GM inequality using induction

  • Math Amateur
  • · Replies 2 ·
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2

Cauchy's inequality: using the discriminant method from Sohrab 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 Bloch theorem 1.4.6: why S ⊆ ℕ from the definition

  • Math Amateur
  • · Replies 7 ·
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7

High School Symmetric Hamiltonian cycle on tesseract graph in 4D

  • DaveC426913
  • · Replies 3 ·
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3

Bloch Theorem 1.4.6: why does S ⊆ ℕ from the definition of ℕ

  • Math Amateur
  • · Replies 4 ·
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4

Bloch Exercise 1.5.9 (3): proving k exists for (r + 1/k)² < s

  • Math Amateur
  • · Replies 2 ·
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2

Proving the sum of a rational and irrational number is irrational

  • Math Amateur
  • · Replies 3 ·
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3

Peano Postulate (a) and why p ≠ 1 in theorem 1.3.7

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Difference between homeomorphisms, homotopies and deformation retracts

  • Silviu
  • · Replies 13 ·
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13