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

Graduate Equation with two unknowns in complex exponential

  • jonasjia
  • · Replies 4 ·
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4

Mapping/determining domain/range

  • nacho-man
  • · Replies 1 ·
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1

Graduate Interchaning Limits and Inner Products

  • logarithmic
  • · Replies 11 ·
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11

Graduate Prove or disprove the following statement using sets frontier points

  • ppy
  • · Replies 4 ·
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4

Problem involving m-tail of a sequence

  • issacnewton
  • · Replies 5 ·
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5

Graduate The space of solutions of the classical wave equation

  • ShayanJ
  • · Replies 3 ·
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3

Graduate Is α an element of B in Rudin's Theorem 1.11?

  • Government$
  • · Replies 5 ·
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5

Undergrad Interior points proof where one set is a subset of the other

  • ppy
  • · Replies 3 ·
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3

Graduate How can I calculate this integral using contour integration?

  • ShayanJ
  • · Replies 1 ·
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1

Difficult Improper Integrals in Real Analysis.

  • bw0young0math
  • · Replies 10 ·
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10

Spivak's Proof Not Clear. Theorem 2.13

  • caffeinemachine
  • · Replies 1 ·
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1

Logarithm and harmonic numbers

  • alyafey22
  • · Replies 2 ·
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2

Which Real Root is Larger: x^8 = 8 - 10x^9 or x^10 = 8 - 10x^11?

  • anemone
  • · Replies 4 ·
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4

Elementary Complex Number Problems

  • nacho-man
  • · Replies 9 ·
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9

Graduate Implicit function theorem for several complex variables

  • Kalidor
  • · Replies 2 ·
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2

Graduate Residue of Dirac delta function?

  • FredMadison
  • · Replies 3 ·
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3

How Do You Compute the Inverse Laplace Transform of a Power Series?

  • nacho-man
  • · Replies 3 ·
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3

What is the correct way to convert to polar form?

  • nacho-man
  • · Replies 4 ·
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4

Prove Continuous Function of t: R^2 to R

  • ryo0071
  • · Replies 3 ·
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3

Help Needed: Preparing for End-of-Semester Math Exam

  • nacho-man
  • · Replies 2 ·
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2

Finding limsup & liminf of Sequence of Sets $A_n$

  • kalish1
  • · Replies 1 ·
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1

Find Complex Conjugate of 1/(1+e^(ix))

  • nicodemus1
  • · Replies 3 ·
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3

Graduate Understanding Completeness of Fourier Basis

  • stephenkeiths
  • · Replies 2 ·
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2

Find Laplace Transform of $ t^2+1)^2 $ without Expansion

  • nacho-man
  • · Replies 5 ·
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5

Graduate Denseness of bounded funtions in L^2?

  • logarithmic
  • · Replies 1 ·
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1

Graduate Please identify a series expansion

  • Jaggis
  • · Replies 1 ·
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1

Graduate Is the Real Field the Only Complete Ordered Field?

  • Bipolarity
  • · Replies 5 ·
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5

Compact Set Question: Counterexample Proved

  • Sudharaka
  • · Replies 4 ·
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4

Undergrad Finding Interior Points in a Subset: Hints & Tips

  • mathanon
  • · Replies 3 ·
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3

Undergrad Question on Taylor expansion of first order

  • mnb96
  • · Replies 8 ·
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8

Graduate Is A a Measurable Set with Sandwich Property?

  • Funky1981
  • · Replies 4 ·
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4

Mobius transformations - I don't get this example

  • nacho-man
  • · Replies 3 ·
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3

Undergrad Is 1/n - 1/(n+k) a Valid Example of a Cauchy Sequence?

  • xdeimos
  • · Replies 2 ·
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2

Graduate I want to show a difference of inner products is small

  • AxiomOfChoice
  • · Replies 5 ·
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5

Discrete sets and uncountability of limit points

  • caffeinemachine
  • · Replies 2 ·
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2

Proving limit of a given sequence

  • issacnewton
  • · Replies 2 ·
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2

Point of convergence of a series

  • caffeinemachine
  • · Replies 2 ·
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2

Graduate Challenge 2: Covering the Triangle

  • Office_Shredder
  • · Replies 27 ·
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27

Graduate Challenge 3b: What's in a polynomial?

  • Office_Shredder
  • · Replies 9 ·
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9

How to graph complex number fractions

  • Raerin
  • · Replies 2 ·
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2

Proving that the sum of 2 measurable functions is measurable

  • oblixps
  • · Replies 4 ·
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4

Graduate Interchanging Linear Operator and Infinite Sum

  • logarithmic
  • · Replies 1 ·
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1

Graph |z| > 3 on the Complex Plane: A Detailed Explanation

  • Raerin
  • · Replies 3 ·
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3

Transforming an integral of Exponential to a Contour

  • shen07
  • · Replies 3 ·
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3

Graduate Equivalence of Log and Argument for Complex Functions?

  • M. next
  • · Replies 8 ·
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8

Is the continuous map property preserved under taking limit points?

  • Sudharaka
  • · Replies 7 ·
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7

Graduate Solving the Integral of $\sin x/x$ with Lebesgue Dominated Convergence

  • Robert1986
  • · Replies 3 ·
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3

Distance between Compact Subsets

  • Sudharaka
  • · Replies 2 ·
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2

Graduate I don't understand this weight fact at all

  • 1MileCrash
  • · Replies 2 ·
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2

Graduate Proving Continuity of y^n Using Induction and the Definition of Continuity

  • Someone2841
  • · Replies 2 ·
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2

Graduate Proof of Continuity of y^2 | Real Analysis I Course

  • Someone2841
  • · Replies 7 ·
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7

Understanding Mapping: Domain, Range & W Subset of C

  • nacho-man
  • · Replies 2 ·
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2

Graduate How Do Complex Numbers Extend the Real Number System?

  • Bipolarity
  • · Replies 2 ·
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2

Graduate A briefing of Topology's most important definitions and results?

  • JPMPhysics
  • · Replies 4 ·
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4

Graduate Is an open map also a homeomorphism?

  • 1MileCrash
  • · Replies 5 ·
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5

Graduate Lebesgue Null Sets: Countable or Not?

  • aaaa202
  • · Replies 1 ·
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1

Graduate Measure theory question: Countable sub-additivity

  • Cascabel
  • · Replies 1 ·
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1

Graduate What does vanishing at infinity mean for a topological space?

  • lugita15
  • · Replies 1 ·
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1

Graduate Dirac Delta Function: Definition & Mathematics

  • Vahsek
  • · Replies 1 ·
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1
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1

Graduate The importance of sigma-algebras

  • aaaa202
  • · Replies 1 ·
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1

Equation of a Circle in the Complex Plane

  • shen07
  • · Replies 5 ·
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5

Graduate Do Hilbert Space Isomorphism Map Dense Sets to Dense Sets?

  • logarithmic
  • · Replies 1 ·
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1

Graduate An inequality for a two variable function

  • amirmath
  • · Replies 1 ·
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1

Can Hölder's Inequality also be applied to other optimization problems?

  • anemone
  • · Replies 2 ·
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2

About fractional parts and floor functions....

  • DreamWeaver
  • · Replies 2 ·
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2

Graduate Can infinity be defined rigorously?

  • dipole
  • · Replies 5 ·
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5

Residue theorem to evaluate integrals

  • nacho-man
  • · Replies 16 ·
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16

Undergrad Need Help With Epsilon Neighbourhoods

  • tanman24
  • · Replies 2 ·
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2

Is There a Real Analysis Method to Solve Complex Integrals?

  • nacho-man
  • · Replies 11 ·
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11

Graduate What Does an Integral Mean in Mathematics?

  • johnqwertyful
  • · Replies 15 ·
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15

Showing the bessel function is entire

  • nacho-man
  • · Replies 2 ·
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2

Expanding to power series, and finding the Laurent Series

  • nacho-man
  • · Replies 5 ·
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5

Graduate Contour Deformation and Jordan's Lemma in Complex Analysis

  • HasuChObe
  • · Replies 2 ·
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2
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5

Find Conformal Map to Remove Semidisk | Solutions & Explanations

  • nacho-man
  • · Replies 1 ·
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1

A Conjecture About Polynomials in Two Variables

  • caffeinemachine
  • · Replies 2 ·
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2

Fourier Transform of a function squared.

  • Dustinsfl
  • · Replies 1 ·
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1

Differentiability of a Complex Function

  • shen07
  • · Replies 5 ·
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5

Fourier Cosine Series: Equivalence for {x}

  • Joystar77
  • · Replies 4 ·
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4

Find Fourier Sin Series for f(x)=1, 0 < x < c

  • Joystar77
  • · Replies 6 ·
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6

Fourier series--showing converges to pi/16

  • Dustinsfl
  • · Replies 3 ·
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3

Graduate Can a Perfect Set Contain an Open Subset?

  • kostas230
  • · Replies 3 ·
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3

Undergrad How Does the Triangle Inequality Transform from Equality to Inequality?

  • Bashyboy
  • · Replies 3 ·
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3

Proving Equality in Real Numbers: The Case of a+b+c=abc

  • anemone
  • · Replies 2 ·
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2

Graduate How Do You Intuitively Understand a Topology?

  • center o bass
  • · Replies 6 ·
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6

High School What Are Complex Numbers?

  • Ijjapwar
  • · Replies 2 ·
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2

Undergrad Wolfram Alpha: all 2nd roots of 1

  • AllyScientific
  • · Replies 10 ·
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10

Graduate Hausdorff dimension of the cantor set

  • hedipaldi
  • · Replies 1 ·
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1

Graduate Continuity of functions from ℝ→ℝ[sup]2[/sup]

  • Jolb
  • · Replies 8 ·
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8

Graduate Other great books like Mathematical Transition by Chartrand

  • medwatt
  • · Replies 1 ·
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1

Graduate Complex-Valued Functions, limits, and conjugates

  • mathsciguy
  • · Replies 7 ·
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7

Undergrad Complex Numbers and Exponents: Is z^0 Always Equal to 1?

  • Hepic
  • · Replies 2 ·
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2

Undergrad Complex Numbers: Defining an Ordered System

  • lostcauses10x
  • · Replies 6 ·
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6

Graduate Can't understand a proof in Rudin

  • kostas230
  • · Replies 3 ·
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3

Graduate Topology of a mathematical plane

  • sydneybself
  • · Replies 6 ·
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6

Graduate Quadratic inequalities for complex variables?

  • mathsciguy
  • · Replies 3 ·
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3

Undergrad Searching 4 graph optimization software

  • AntistatiK
  • · Replies 2 ·
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2

Graduate Understanding the concept of every open set being a disjoint union

  • jdinatale
  • · Replies 3 ·
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3

Graduate Do open sets in R^2 always have continuous boundaries?

  • lugita15
  • · Replies 6 ·
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6