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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Graduate Complex Analysis - Fibonacci Identity

  • Physics-Pure
  • · Replies 17 ·
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17

Undergrad Can irrational numbers exist on the numberline?

  • Mu naught
  • · Replies 41 ·
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41

Graduate A fundamental question on homeomorphism

  • krete
  • · Replies 5 ·
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5

Graduate Prove f is in L3(dμ): Measurable Function

  • hedipaldi
  • · Replies 1 ·
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1

Is This Integral Really Too Difficult to Solve?

  • chisigma
  • · Replies 6 ·
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6

Graduate Understanding Quotient Spaces of Triangles

  • iLoveTopology
  • · Replies 2 ·
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2

How to Analyze Series Convergence with a Floor Function?

  • Lisa91
  • · Replies 11 ·
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11

Undergrad A continuous function having an inverse <=> conditions on a derivative?

  • hb1547
  • · Replies 2 ·
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2

Graduate What is Homeomorphism Type? Definition & Examples

  • iLoveTopology
  • · Replies 1 ·
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1
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6

Is f a Contraction Mapping on [1,∞)?

  • Poirot1
  • · Replies 1 ·
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1

Series Multiplication: Investigate Convergence

  • Lisa91
  • · Replies 3 ·
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3

Graduate Munkres Topology - Chapter 7 - Complete Metric Spaces and Function Spaces

  • sammycaps
  • · Replies 2 ·
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2

Graduate What Causes the Error in Calculating the L2 Norm of Complex Functions?

  • divB
  • · Replies 5 ·
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5

Graduate How is a discrete topology a 0-manifold?

  • dumbQuestion
  • · Replies 1 ·
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1

Graduate Understanding the Real Inner Product in Linear Algebra and Fourier Analysis

  • member 428835
  • · Replies 5 ·
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5

Find the standard form of conic

  • Poirot1
  • · Replies 1 ·
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1

Logical error in Spivak's Calculus?

  • nimon
  • · Replies 2 ·
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2

Graduate Fourier series: relation of coefficients

  • divB
  • · Replies 3 ·
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3

Graduate Solve Complex Equation: Find Z, K in \frac{Z-a}{Z-b}=Ke^{±jθ}

  • powers
  • · Replies 3 ·
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3

Least upper bound - greatest lower bound duality

  • OhMyMarkov
  • · Replies 1 ·
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1

Graduate Cantor Set - Perfect and Totally Disconnected

  • The5ifthColumn
  • · Replies 8 ·
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8

Strange inequality of infinite series

  • pantboio
  • · Replies 4 ·
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4

Graduate Locally Compact Hausdorff Space is Regular

  • sammycaps
  • · Replies 4 ·
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4

Graduate Is There a Shape with More than 2^{\aleph_0} Sides in the Euclidean Plane?

  • cragar
  • · Replies 3 ·
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3

Exponent of convergence of a sequence of complex numbers

  • pantboio
  • · Replies 2 ·
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2

Graduate Find Exterior Derivative of Differential Forms in Dim > 3

  • saminator910
  • · Replies 7 ·
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7

Showing that nth root of c_n is equal to nth root of c_n+1 in the limit

  • OhMyMarkov
  • · Replies 2 ·
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2

On proving sup A is less than sup B when A is in B

  • OhMyMarkov
  • · Replies 2 ·
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2

Graduate Radius of Convergence: Complex Series Need Not Be Defined Everywhere

  • freddyfish
  • · Replies 3 ·
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3

Showing that lim_sup a_n b_n = lim a_n lim_sup b_n$

  • OhMyMarkov
  • · Replies 1 ·
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1

Proving lim sqrt(n) alpha^n is 0

  • OhMyMarkov
  • · Replies 1 ·
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1

Undergrad How Do You Convert a Complex Spiral Equation from Polar to Cartesian Form?

  • Rohitpi
  • · Replies 2 ·
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2

Graduate Are Topological and Algebraic Closures Related?

  • Bachelier
  • · Replies 8 ·
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8

Graduate Is there a coordinate independent Dirac delta function?

  • friend
  • · Replies 5 ·
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5

Graduate Prove Rudin's Theorem 2.27: Closure of E in Metric Space X is Closed

  • Bachelier
  • · Replies 11 ·
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11

Graduate Does integration require a metric?

  • friend
  • · Replies 9 ·
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9

Supremum of f(x) on [a,b] vs. supremum of f(x+c) on [a+c, b+c]

  • OhMyMarkov
  • · Replies 7 ·
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7
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1

Graduate Difference of closures is subset of closure of difference

  • Rasalhague
  • · Replies 4 ·
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4

Supremum Proof Concerning Sqrt[2]

  • MI6
  • · Replies 2 ·
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2

Graduate Differential of a function vs differential forms

  • Damidami
  • · Replies 1 ·
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1

Undergrad Simple complex power: why is e^( i (2*Pi*n*t)/T ) not 1?

  • Aziza
  • · Replies 4 ·
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4

Graduate When can interchange sum and integral

  • Aziza
  • · Replies 2 ·
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2

Undergrad On solving for a variable in the magnitude of a complex number

  • Jeff Cook
  • · Replies 11 ·
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11

Differentiating an integral wrt a function

  • OhMyMarkov
  • · Replies 3 ·
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3

Graduate How Does the Density of Q in R Get Proven in Rudin's Analysis?

  • kostas230
  • · Replies 2 ·
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2

Graduate Proof of existence of nonmeasurable sets

  • mathmonkey
  • · Replies 2 ·
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2

Undergrad Is 1 Included in the Mathematical Set S?

  • Bachelier
  • · Replies 4 ·
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4

Graduate Confusion regarding Residue Theorem

  • Mr. Heretic
  • · Replies 8 ·
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8

Proving $\text{diam}(A)=\text{diam}(\overline A)$ for Metric Spaces

  • Ubistvo
  • · Replies 3 ·
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3

Graduate How to find the cosine of i using Taylor series?

  • pierce15
  • · Replies 7 ·
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7

Is Every Continuous Function on [-1,1] Riemann-Integrable?

  • mm1239
  • · Replies 7 ·
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7

Graduate Eigenvalues of a compact positive definite operator

  • SVD
  • · Replies 2 ·
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2

Correcting Constants in Convolution of Fourier Transforms

  • Dustinsfl
  • · Replies 17 ·
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17

Solve for A_n: Fourier Coefficient $$u_y(x,\pi) = 0$$

  • Dustinsfl
  • · Replies 1 ·
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1

Undergrad What should be the influence of the imaginary part on a complex number?

  • pseudorandom
  • · Replies 2 ·
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2

Imaginary Part of a Complex Function: How to Find It?

  • Poly1
  • · Replies 2 ·
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2

Dirichlet problem for the laplacian in the strip

  • pantboio
  • · Replies 1 ·
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1

Graduate Convergent sequence in compact metric space

  • pob1212
  • · Replies 4 ·
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4

Undergrad Solving for ΔP: Should I Include ΔVΔI?

  • Kyouran
  • · Replies 1 ·
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1

Linear fractional transformation fixing a line

  • pantboio
  • · Replies 11 ·
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11

Graduate Types of points in metric spaces

  • pob1212
  • · Replies 1 ·
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1

Graduate Are Quotients by Homeomorphic Subspaces Homeomorphic?

  • WWGD
  • · Replies 11 ·
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11

Integrating delta/Bessel function

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Why Did Radon Choose Riemann-Stieltjes Over Lebesgue Integration?

  • jsr9119
  • · Replies 5 ·
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5

Set equality with a function and its inverse.

  • OhMyMarkov
  • · Replies 2 ·
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2

If Σc_nx^n converges does Σc_n·nx^(n-1) converge as well?

  • OhMyMarkov
  • · Replies 6 ·
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6

Taylor Series: Exploring Properties & Applications

  • OhMyMarkov
  • · Replies 11 ·
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11

Graduate Dirac Distribution with 2 Diracs

  • divB
  • · Replies 2 ·
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2

Graduate How can we redefine limits to remove problems with the current definition?

  • ato
  • · Replies 33 ·
2
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33

Why is the following not true: f(f^(-1)(B))=B?

  • OhMyMarkov
  • · Replies 1 ·
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1
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6

Graduate Considering the hypothetical distance between consecutive reals.

  • hddd123456789
  • · Replies 7 ·
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7

Singularities, Residues, and Computation: Analyzing $f(z)$ without Prefix

  • pantboio
  • · Replies 4 ·
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4

Some Contour Integration Questions

  • thatonekid
  • · Replies 1 ·
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1

Complex Analysis Review Question

  • thatonekid
  • · Replies 5 ·
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5

Is the Inverse of a Function Always Well-Defined?

  • OhMyMarkov
  • · Replies 3 ·
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3

Graduate How Can Different Definitions of Separating Families of Seminorms Be Reconciled?

  • julian
  • · Replies 1 ·
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1

Graduate What Are Riemann-Stieltjes Integrals and How Can We Visualize Them?

  • Artusartos
  • · Replies 3 ·
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3

Double Fourier Series for Bivariate Functions

  • Dustinsfl
  • · Replies 17 ·
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17

Graduate Is There a Way to Reverse Substitution in Finding Zeroes?

  • pierce15
  • · Replies 5 ·
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5

Graduate Radius of convergence without complex numbers

  • rsq_a
  • · Replies 22 ·
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22

Graduate Is Every Metric Space Hausdorff?

  • Dead Boss
  • · Replies 2 ·
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2

Graduate Absolutely convergent but not uniformly convergent

  • samithie
  • · Replies 1 ·
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1

If f is holomorphic, is Σf(z^k) holomorphic?

  • pantboio
  • · Replies 5 ·
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5

Graduate Differentiability of a Series of Functions

  • luke8ball
  • · Replies 1 ·
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1

Graduate Fourier series of functions with points of discontinuity

  • jorgdv
  • · Replies 9 ·
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9

Solving Real Number Variables & Parabola Equations

  • DrunkenOldFool
  • · Replies 1 ·
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1

Graduate Theorem connecting the inverse of a holomorphic function to a contour integral

  • IDontKnow1
  • · Replies 1 ·
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1

Graduate How can the exact values of the W function be calculated for all numbers?

  • pierce15
  • · Replies 5 ·
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5

Graduate How to show that the operation of a group is continuous?

  • Arian.D
  • · Replies 7 ·
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7

Undergrad Finding (2+6i)^(1/3): Proving a+bi Assumption is Correct

  • Outrageous
  • · Replies 6 ·
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6

Graduate In a sequence of all rationals, why is every real number a subsequential limit?

  • docholliday
  • · Replies 4 ·
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4

What is lim_(n→∞) ∫_(-∞)^∞〖〖 x〗^n e^(-n|x|) dm 〗?

  • Jack3
  • · Replies 3 ·
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3

Undergrad Closed and bounded in relation to compact

  • trap101
  • · Replies 9 ·
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9

Does this series converge almost everywhere?

  • Jack3
  • · Replies 2 ·
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2

Undergrad Convexity of a function I don't understand

  • newphysist
  • · Replies 1 ·
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1

How should I show that lim_n ∫〖f_n dm〗 = ∫〖f dm〗?

  • Jack3
  • · Replies 1 ·
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1
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1