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

An integral representation of the Riemann zeta function

  • polygamma
  • · Replies 1 ·
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1

Geometric Puzzle: Find P & Q in R2 Square

  • HallsofIvy
  • · Replies 2 ·
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2

Graduate Why Are the Definitions of Hausdorff Dimension Equivalent?

  • hedipaldi
  • · Replies 1 ·
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1

Graduate The pure-point subspace of a Hilbert space is closed

  • AxiomOfChoice
  • · Replies 3 ·
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3

Finding the real and imaginary parts of a function

  • shen07
  • · Replies 6 ·
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6

Can You Solve This Challenging Functional Equation?

  • MarkFL
  • · Replies 14 ·
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14

Graduate The nature of the dirac delta function

  • sgfw
  • · Replies 8 ·
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8

Undergrad Please explain why z = cosθ + jsinθ in this video.

  • anhnha
  • · Replies 7 ·
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7

Inequality Proof: Fun Problem | z,w <1 | Forum

  • SweatingBear
  • · Replies 6 ·
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6

Can you please tell me if this question is Correct?

  • shen07
  • · Replies 4 ·
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4

Undergrad Rethinking Complex Numbers: A New Perspective on Teaching and Understanding

  • meBigGuy
  • · Replies 24 ·
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24

Solving Complex Expressions for Scientists

  • shen07
  • · Replies 9 ·
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9

Graduate Can a Non-Monotonic, Bounded Function Have a Limit?

  • DeadOriginal
  • · Replies 8 ·
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8

Graduate How Does Knot Theory Connect with Other Fields and Real-World Applications?

  • modnarandom
  • · Replies 1 ·
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1

Ambiguity in the Arc-Tangent Function

  • bw0young0math
  • · Replies 3 ·
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3

Graduate Where Can I Find Information on Non-Trivial Zeros and Meromorphic Functions?

  • greentea28a
  • · Replies 1 ·
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1

What Are the Possible Values of 2^(-i)?

  • shen07
  • · Replies 10 ·
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10

Can a sequence without a convergent subsequence have a limit of infinity?

  • Fernando Revilla
  • · Replies 4 ·
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4

Sum of squares of average change is less than

  • caffeinemachine
  • · Replies 3 ·
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3

Undergrad Finding Amplitude and Phase of Complex Functions

  • hogrampage
  • · Replies 1 ·
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1

Graduate Complex conjugates of functions

  • brmath
  • · Replies 2 ·
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2

Undergrad What is the concept of fractal dimension and how is it computed?

  • hedipaldi
  • · Replies 1 ·
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1

Graduate Why is this expression bounded by 1?

  • AxiomOfChoice
  • · Replies 3 ·
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3

Graduate When Does Set-Theoretic Logic Hold for Infinite Sets?

  • jetplan
  • · Replies 8 ·
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8

Graduate Understanding Riemann Surfaces and Their Applications in Complex Analysis

  • Mandelbroth
  • · Replies 7 ·
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7

Graduate How can I prove that this 2D expression is always less than 1 for n≠β?

  • Karthiksrao
  • · Replies 2 ·
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2

Proof of 1+z+Z^2+...+z^n=(1-z^(n+1))/(1-z)

  • shen07
  • · Replies 3 ·
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3

Find Residues for f(z) at $z=-n$

  • alyafey22
  • · Replies 2 ·
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2

Graduate Does L^2 Convergance Imply Convergance of L^2 norms?

  • logarithmic
  • · Replies 1 ·
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1

Graduate Challenge VIII: Discontinuities of a function solved by Theorem.

  • micromass
  • · Replies 17 ·
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17

How many real and non-real roots?

  • SweatingBear
  • · Replies 8 ·
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8

Graduate The closure of an open set A, strictly bigger than A itself?

  • adam512
  • · Replies 5 ·
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5

Help with Proof: Sum of Cosines Up to n Terms

  • shen07
  • · Replies 4 ·
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4

Graduate Unboundness and periodicity for complex trig functions

  • ppy
  • · Replies 4 ·
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4

Graduate Do Tensor Product Properties Hold in Infinite Dimensional Hilbert Spaces?

  • LagrangeEuler
  • · Replies 1 ·
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1

Correspondence between Arc Lengths and Real Numbers in Trigonometry

  • paulmdrdo1
  • · Replies 7 ·
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7

Homeomorphism between a cylinder and a plane?

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate Is There a Non-Calculus Method to Prove this Thermodynamic Inequality?

  • emroz92
  • · Replies 3 ·
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3

Which Real Numbers Intersect This Curve at Four Distinct Points?

  • anemone
  • · Replies 2 ·
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2

Graduate Generalization of Mean Value Theorem for Integrals Needed

  • Only a Mirage
  • · Replies 3 ·
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3

Graduate Some introductory Topology questions

  • 1MileCrash
  • · Replies 98 ·
4
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98

Graduate A countable subset of an infinite set and the axiom of choice.

  • gottfried
  • · Replies 3 ·
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3

Graduate Lebesgue measure and the Banch-Tarski Paradox

  • gottfried
  • · Replies 8 ·
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8

Graduate How Does Orthogonal Projection Work in L^2 Spaces with a Self-Adjoint Operator?

  • AxiomOfChoice
  • · Replies 5 ·
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5

Graduate Complex integral is zero but fn. is not analytic

  • ppy
  • · Replies 5 ·
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5

Graduate Challenge IV: Complex Square Roots, solved by jgens

  • micromass
  • · Replies 9 ·
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9

Graduate How Can Norm Integration Address Inequality?

  • nalkapo
  • · Replies 3 ·
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3

Infinite Product: Showing & Evaluating

  • polygamma
  • · Replies 8 ·
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8

Graduate Bounds on infinite sequences with a known limit

  • Nelphine
  • · Replies 5 ·
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5

Irrational numbers forming dense subset

  • bw0young0math
  • · Replies 1 ·
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1

Problem about finding sup of a set

  • issacnewton
  • · Replies 5 ·
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5

Undergrad Proof about complex conjugate of a function

  • anhnha
  • · Replies 7 ·
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7

Graduate Finding large order spherical harmonics

  • alemsalem
  • · Replies 2 ·
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2

Graduate What Causes the Complex Number Paradox in Mathematics?

  • bgq
  • · Replies 23 ·
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23

Graduate Show that an open connected subset of R^2 is path-connected

  • adam512
  • · Replies 9 ·
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9

Graduate Equivalent conditions for a measurability restriction?

  • economicsnerd
  • · Replies 5 ·
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5

Graduate Equal partition Integral problem

  • subsonicman
  • · Replies 9 ·
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9

Graduate Lipschitz vs uniform continuity.

  • gottfried
  • · Replies 1 ·
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1

Graduate Could we have negative dimensions?

  • MathematicalPhysicist
  • · Replies 2 ·
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2

Graduate Complex analysis book with lots of solved problems?

  • stgermaine
  • · Replies 1 ·
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1

Do we have identities for the inverse tangent function for complex numbers?

  • alyafey22
  • · Replies 4 ·
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4

Graduate Are Abelian fundamental groups always isomorphic in path connected spaces?

  • R136a1
  • · Replies 1 ·
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1

Graduate Is Every Closed Subset of ##\mathbb{R}^2## the Boundary of Some Set?

  • R136a1
  • · Replies 9 ·
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9

What are the $\rho$ values in the zeros of the Zeta function?

  • mathworker
  • · Replies 1 ·
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1

Liouville's extension of Dirichlet's theorem

  • ksananthu
  • · Replies 3 ·
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3

Graduate Can the rational numbers be embedded in a countable complete metric space X?

  • hedipaldi
  • · Replies 17 ·
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17

Inequality--is there an elegant way to solve this?

  • Dustinsfl
  • · Replies 4 ·
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4

Which Book Should I Choose for Starting Complex Analysis?

  • caffeinemachine
  • · Replies 7 ·
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7

Exact Differential: Show f(z)dz is Exact

  • ssh
  • · Replies 1 ·
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1

Graduate Why is 4 Colors Sufficient to Color a 2D Map?

  • Natron
  • · Replies 1 ·
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1

Continuous mapping of compact metric spaces

  • alyafey22
  • · Replies 6 ·
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6

Graduate Some questions about topological groups

  • R136a1
  • · Replies 2 ·
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2

Graduate Are Maps on a Sphere Homotopic if They Avoid Antipodal Points?

  • R136a1
  • · Replies 4 ·
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4

Graduate Is the maximum of infinitely many functions continuous on a compact space?

  • R136a1
  • · Replies 8 ·
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8

Graduate Integral Inequality for Measurable Functions

  • amirmath
  • · Replies 1 ·
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1

Graduate Homeomorphism of Unit Circle and XxX Product Space

  • hedipaldi
  • · Replies 2 ·
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2

Graduate Evaluate Integral of Bessel K Function

  • kschau
  • · Replies 2 ·
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2

Compactness Theorem: Intersection of Compact Sets

  • alyafey22
  • · Replies 5 ·
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5

Graduate Box topology does not preserve first countable

  • R136a1
  • · Replies 3 ·
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3

Graduate Hausdorff Spaces: Does Convergence to One Point Characterize?

  • R136a1
  • · Replies 2 ·
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2

Real & Complex Analysis: Beginner's Guide

  • mathworker
  • · Replies 6 ·
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6

Graduate Does a second countable space have a converging sequence in its closure?

  • R136a1
  • · Replies 6 ·
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6

Graduate Graph of f:[0,1]->R compact <=> f continuous

  • dumbQuestion
  • · Replies 5 ·
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5

Graduate The difference between the limits of two Cauchy Sequences

  • ANphysics
  • · Replies 13 ·
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13

Graduate Prove Compact Metric Space is Locally Path Connected

  • hedipaldi
  • · Replies 4 ·
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4

Graduate Open sets in the product topology

  • dumbQuestion
  • · Replies 1 ·
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1

Graduate Cont image of connected space is connected proof check?

  • dumbQuestion
  • · Replies 2 ·
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2

Graduate A problem about non-separable Hilbert space

  • prophetlmn
  • · Replies 7 ·
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7

Graduate Find a 2-arguments function from six constraints on its derivatives

  • GreenZorg
  • · Replies 4 ·
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4

Prove Log Gamma Integral: $\sqrt{2 \pi}$

  • alyafey22
  • · Replies 2 ·
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2

Graduate Homeomorphism through cutting and pasting of manifolds

  • Mr-T
  • · Replies 9 ·
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9

Graduate Why is the Twin Primes Conjecture still relevant to mathematicians today?

  • mathnerd15
  • · Replies 8 ·
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8

Lagrange's Identity and Cauhchy-Schwarz Inequality for complex numbers

  • rmcknigh
  • · Replies 1 ·
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1

Prove 7.81: Contour Integration for Schaum's Outline Series

  • alyafey22
  • · Replies 6 ·
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6

Graduate Why Isn't the Sum of Grandi's Series Zero?

  • Natron
  • · Replies 8 ·
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8

Undergrad A proof regarding Rational numbers

  • thudda
  • · Replies 4 ·
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4

Graduate Problem in understanding the meaning

  • thudda
  • · Replies 4 ·
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4

Graduate Matrix-valued analytic function?

  • AxiomOfChoice
  • · Replies 2 ·
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2

Graduate Analytical solution of an infinite series

  • Matheco
  • · Replies 3 ·
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3

Graduate Residue of Function f(z)=e1/z/(1-z): Guide and Explanation

  • aiisshsaak
  • · Replies 15 ·
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15